Release 0.18.0-dev (development release)

New features since last release

Custom gradient transforms can now be created using the new @qml.gradients.gradient_transform decorator on a batch-tape transform. (#1589)

Quantum gradient transforms are a specific case of qml.batch_transform. All quantum gradient transforms accept a tape, and outputs a batch of tapes to be independently executed on a quantum device, alongside a post-processing function that returns the result.

Furthermore, a smart default expansion function is provided, which automatically expands tape operations which are not differentiable prior to applying the quantum gradient. All gradient transforms in qml.gradients are now decorated with this decorator.

Supported gradient transforms must be of the following form:
```
@qml.gradients.gradient_transform
def my_custom_gradient(tape, argnum=None, **kwargs):
    ...
    return gradient_tapes, processing_fn
```
Once defined, quantum gradient transforms can be applied directly to QNodes:
```
>>> @qml.qnode(dev)
... def circuit(x):
...     qml.RX(x, wires=0)
...     qml.CNOT(wires=[0, 1])
...     return qml.expval(qml.PauliZ(0))
>>> circuit(0.3)
tensor(0.95533649, requires_grad=True)
>>> qml.gradients.param_shift(circuit)(0.5)
array([[-0.47942554]])
```
Quantum gradient transforms are fully differentiable, allowing higher order derivatives to be accessed:
```
>>> qml.grad(qml.gradients.param_shift(circuit))(0.5)
tensor(-0.87758256, requires_grad=True)
```

The ability to define batch transforms has been added via the new @qml.batch_transform decorator. (#1493)

A batch transform is a transform that takes a single tape or QNode as input, and executes multiple tapes or QNodes independently. The results may then be post-processed before being returned.

For example, consider the following batch transform:

@qml.batch_transform
def my_transform(tape, a, b):
    """Generates two tapes, one with all RX replaced with RY,
    and the other with all RX replaced with RZ."""
    tape1 = qml.tape.JacobianTape()
    tape2 = qml.tape.JacobianTape()

    # loop through all operations on the input tape
    for op in tape.operations + tape.measurements:
        if op.name == "RX":
            with tape1:
                qml.RY(a * qml.math.abs(op.parameters[0]), wires=op.wires)
            with tape2:
                qml.RZ(b * qml.math.abs(op.parameters[0]), wires=op.wires)
        else:
            for t in [tape1, tape2]:
                with t:
                    qml.apply(op)

    def processing_fn(results):
        return qml.math.sum(qml.math.stack(results))

    return [tape1, tape2], processing_fn

We can transform a QNode directly using decorator syntax:

>>> @my_transform(0.65, 2.5)
... @qml.qnode(dev)
... def circuit(x):
...     qml.Hadamard(wires=0)
...     qml.RX(x, wires=0)
...     return qml.expval(qml.PauliX(0))
>>> print(circuit(-0.5))
1.2629730888100839

Batch tape transforms are fully differentiable:

>>> gradient = qml.grad(circuit)(-0.5)
>>> print(gradient)
2.5800122591960153

Batch transforms can also be applied to existing QNodes,

>>> new_qnode = my_transform(existing_qnode, *transform_weights)
>>> new_qnode(weights)

or to tapes (in which case, the processed tapes and classical post-processing functions are returned):

>>> tapes, fn = my_transform(tape, 0.65, 2.5)
>>> from pennylane.interfaces.batch import execute
>>> dev = qml.device("default.qubit", wires=1)
>>> res = execute(tapes, dev, interface="autograd", gradient_fn=qml.gradients.param_shift)
1.2629730888100839

Added a new SISWAP operation and a SQISW alias with support to the default_qubit device. #1563

The RotosolveOptimizer now can tackle general parametrized circuits, and is no longer restricted to single-qubit Pauli rotations. (#1489)

This includes:

layers of gates controlled by the same parameter,
controlled variants of parametrized gates, and
Hamiltonian time evolution.

Note that the eigenvalue spectrum of the gate generator needs to be known to use RotosolveOptimizer for a general gate, and it is required to produce equidistant frequencies. For details see Vidal and Theis, 2018 and Wierichs, Izaac, Wang, Lin 2021.

Consider a circuit with a mixture of Pauli rotation gates, controlled Pauli rotations, and single-parameter layers of Pauli rotations:

dev = qml.device('default.qubit', wires=3, shots=None)

@qml.qnode(dev)
def cost_function(rot_param, layer_par, crot_param):
    for i, par in enumerate(rot_param):
        qml.RX(par, wires=i)
    for w in dev.wires:
        qml.RX(layer_par, wires=w)
    for i, par in enumerate(crot_param):
        qml.CRY(par, wires=[i, (i+1) % 3])

    return qml.expval(qml.PauliZ(0) @ qml.PauliZ(1) @ qml.PauliZ(2))

This cost function has one frequency for each of the first RX rotation angles, three frequencies for the layer of RX gates that depend on layer_par, and two frequencies for each of the CRY gate parameters. Rotosolve can then be used to minimize the cost_function:

# Initial parameters
init_param = [
    np.array([0.3, 0.2, 0.67], requires_grad=True),
    np.array(1.1, requires_grad=True),
    np.array([-0.2, 0.1, -2.5], requires_grad=True),
]
# Numbers of frequencies per parameter
num_freqs = [[1, 1, 1], 3, [2, 2, 2]]

opt = qml.RotosolveOptimizer()
param = init_param.copy()

In addition, the optimization technique for the Rotosolve substeps can be chosen via the optimizer and optimizer_kwargs keyword arguments and the minimized cost of the intermediate univariate reconstructions can be read out via full_output, including the cost after the full Rotosolve step:

for step in range(3):
    param, cost, sub_cost = opt.step_and_cost(
        cost_function,
        *param,
        num_freqs=num_freqs,
        full_output=True,
        optimizer="brute",
    )
    print(f"Cost before step: {cost}")
    print(f"Minimization substeps: {np.round(sub_cost, 6)}")

Cost before step: 0.042008210392535605
Minimization substeps: [-0.230905 -0.863336 -0.980072 -0.980072 -1.       -1.       -1.      ]
Cost before step: -0.999999999068121
Minimization substeps: [-1. -1. -1. -1. -1. -1. -1.]
Cost before step: -1.0
Minimization substeps: [-1. -1. -1. -1. -1. -1. -1.]

For usage details please consider the docstring.

The frobenius_inner_product function has been moved to the qml.math module, and is now differentiable using all autodiff frameworks. (#1388)
Vector-Jacobian product transforms have been added to the qml.gradients package. (#1494)

The new transforms include:
- qml.gradients.vjp
- qml.gradients.batch_vjp
The Hamiltonian can now store grouping information, which can be accessed by a device to speed up computations of the expectation value of a Hamiltonian. (#1515)
```
obs = [qml.PauliX(0), qml.PauliX(1), qml.PauliZ(0)]
coeffs = np.array([1., 2., 3.])
H = qml.Hamiltonian(coeffs, obs, grouping_type='qwc')
```
Initialization with a grouping_type other than None stores the indices required to make groups of commuting observables and their coefficients.
```
>>> H.grouping_indices
[[0, 1], [2]]
```

Hamiltonians are now trainable with respect to their coefficients. (#1483)

from pennylane import numpy as np

dev = qml.device("default.qubit", wires=2)
@qml.qnode(dev)
def circuit(coeffs, param):
    qml.RX(param, wires=0)
    qml.RY(param, wires=0)
    return qml.expval(
        qml.Hamiltonian(coeffs, [qml.PauliX(0), qml.PauliZ(0)], simplify=True)
    )

coeffs = np.array([-0.05, 0.17])
param = np.array(1.7)
grad_fn = qml.grad(circuit)

>>> grad_fn(coeffs, param)
(array([-0.12777055,  0.0166009 ]), array(0.0917819))

Support for differentiable execution of batches of circuits has been added, via the beta pennylane.interfaces.batch module. (#1501) (#1508) (#1542) (#1549)

For example:

from pennylane.interfaces.batch import execute

def cost_fn(x):
    with qml.tape.JacobianTape() as tape1:
        qml.RX(x[0], wires=[0])
        qml.RY(x[1], wires=[1])
        qml.CNOT(wires=[0, 1])
        qml.var(qml.PauliZ(0) @ qml.PauliX(1))

    with qml.tape.JacobianTape() as tape2:
        qml.RX(x[0], wires=0)
        qml.RY(x[0], wires=1)
        qml.CNOT(wires=[0, 1])
        qml.probs(wires=1)

    result = execute(
        [tape1, tape2], dev,
        gradient_fn=qml.gradients.param_shift,
        interface="autograd"
    )
    return result[0] + result[1][0, 0]

res = qml.grad(cost_fn)(params)

Improvements

The device test suite has been expanded to cover more qubit operations and observables. (#1510)
The MultiControlledX class now inherits from Operation instead of ControlledQubitUnitary which makes the MultiControlledX gate a non-parameterized gate. (#1557)
The utils.sparse_hamiltonian function can now deal with non-integer wire labels, and it throws an error for the edge case of observables that are created from multi-qubit operations. (#1550)
Added the matrix attribute to qml.templates.subroutines.GroverOperator (#1553)
The tape.to_openqasm() method now has a measure_all argument that specifies whether the serialized OpenQASM script includes computational basis measurements on all of the qubits or just those specified by the tape. (#1559)
An error is raised when no arguments are passed to a qml.operation.Observable to inform the user about specifying wires. (#1547)
The Hamiltonian class was moved to the ops/qubit folder from the vqe module, since it is now an observable. (#1534)

The group_observables transform is now differentiable. (#1483)

For example:

import jax
from jax import numpy as jnp

coeffs = jnp.array([1., 2., 3.])
obs = [PauliX(wires=0), PauliX(wires=1), PauliZ(wires=1)]

def group(coeffs, select=None):
  _, grouped_coeffs = qml.grouping.group_observables(obs, coeffs)
  # in this example, grouped_coeffs is a list of two jax tensors
  # [DeviceArray([1., 2.], dtype=float32), DeviceArray([3.], dtype=float32)]
  return grouped_coeffs[select]

jac_fn = jax.jacobian(group)

>>> jac_fn(coeffs, select=0)
[[1. 0. 0.]
[0. 1. 0.]]

>>> jac_fn(coeffs, select=1)
[[0., 0., 1.]]

The tape does not verify any more that all Observables have owners in the annotated queue. (#1505)

This allows manipulation of Observables inside a tape context. An example is expval(Tensor(qml.PauliX(0), qml.Identity(1)).prune()) which makes the expval an owner of the pruned tensor and its constituent observables, but leaves the original tensor in the queue without an owner.
Create a separate requirements file for the CI issue , to have a separate requirements.txt (pinned) and requirements-ci.txt (unpinned). This latter would be used by the CI. (#1535)
The QFT operation is moved to template (#1548)
The qml.ResetError is now supported for default.mixed device. (#1541)

Breaking changes

The class qml.Interferometer is deprecated and will be renamed qml.InterferometerUnitary after one release cycle. (#1546)

Bug fixes

Fix bug when computing expectations of Hamiltonians using TensorFlow. (#1586)
Fix bug when computing the specs of a circuit with a Hamiltonian observable. (#1533)

Documentation

The qml.Identity operation is placed under the sections Qubit observables and CV observables. (#1576)
Updated the documentation of qml.grouping, qml.kernels and qml.qaoa modules to present the list of functions first followed by the technical details of the module. (#1581)
Recategorized Qubit operations into new and existing categories so that code for each operation is easier to locate. (#1566)

Contributors

This release contains contributions from (in alphabetical order):

Vishnu Ajith, Akash Narayanan B, Thomas Bromley, Tanya Garg, Josh Izaac, Prateek Jain, Johannes Jakob Meyer, Pratul Saini, Maria Schuld, Ingrid Strandberg, David Wierichs, Vincent Wong.

Release 0.17.0 (current release)

New features since the last release

Circuit optimization

PennyLane can now perform quantum circuit optimization using the top-level transform qml.compile. The compile transform allows you to chain together sequences of tape and quantum function transforms into custom circuit optimization pipelines. (#1475)

For example, take the following decorated quantum function:

dev = qml.device('default.qubit', wires=[0, 1, 2])

@qml.qnode(dev)
@qml.compile()
def qfunc(x, y, z):
    qml.Hadamard(wires=0)
    qml.Hadamard(wires=1)
    qml.Hadamard(wires=2)
    qml.RZ(z, wires=2)
    qml.CNOT(wires=[2, 1])
    qml.RX(z, wires=0)
    qml.CNOT(wires=[1, 0])
    qml.RX(x, wires=0)
    qml.CNOT(wires=[1, 0])
    qml.RZ(-z, wires=2)
    qml.RX(y, wires=2)
    qml.PauliY(wires=2)
    qml.CZ(wires=[1, 2])
    return qml.expval(qml.PauliZ(wires=0))

The default behaviour of qml.compile is to apply a sequence of three transforms: commute_controlled, cancel_inverses, and then merge_rotations.

>>> print(qml.draw(qfunc)(0.2, 0.3, 0.4))
 0: ──H───RX(0.6)──────────────────┤ ⟨Z⟩
 1: ──H──╭X────────────────────╭C──┤
 2: ──H──╰C────────RX(0.3)──Y──╰Z──┤

The qml.compile transform is flexible and accepts a custom pipeline of tape and quantum function transforms (you can even write your own!). For example, if we wanted to only push single-qubit gates through controlled gates and cancel adjacent inverses, we could do:

from pennylane.transforms import commute_controlled, cancel_inverses
pipeline = [commute_controlled, cancel_inverses]

@qml.qnode(dev)
@qml.compile(pipeline=pipeline)
def qfunc(x, y, z):
    qml.Hadamard(wires=0)
    qml.Hadamard(wires=1)
    qml.Hadamard(wires=2)
    qml.RZ(z, wires=2)
    qml.CNOT(wires=[2, 1])
    qml.RX(z, wires=0)
    qml.CNOT(wires=[1, 0])
    qml.RX(x, wires=0)
    qml.CNOT(wires=[1, 0])
    qml.RZ(-z, wires=2)
    qml.RX(y, wires=2)
    qml.PauliY(wires=2)
    qml.CZ(wires=[1, 2])
    return qml.expval(qml.PauliZ(wires=0))

>>> print(qml.draw(qfunc)(0.2, 0.3, 0.4))
 0: ──H───RX(0.4)──RX(0.2)────────────────────────────┤ ⟨Z⟩
 1: ──H──╭X───────────────────────────────────────╭C──┤
 2: ──H──╰C────────RZ(0.4)──RZ(-0.4)──RX(0.3)──Y──╰Z──┤

The following compilation transforms have been added and are also available to use, either independently, or within a qml.compile pipeline:

commute_controlled: push commuting single-qubit gates through controlled operations. (#1464)
cancel_inverses: removes adjacent pairs of operations that cancel out. (#1455)
merge_rotations: combines adjacent rotation gates of the same type into a single gate, including controlled rotations. (#1455)
single_qubit_fusion: acts on all sequences of single-qubit operations in a quantum function, and converts each sequence to a single Rot gate. (#1458)

For more details on qml.compile and the available compilation transforms, see the compilation documentation.

QNodes are even more powerful

Computational basis samples directly from the underlying device can now be returned directly from QNodes via qml.sample(). (#1441)

dev = qml.device("default.qubit", wires=3, shots=5)

@qml.qnode(dev)
def circuit_1():
    qml.Hadamard(wires=0)
    qml.Hadamard(wires=1)
    return qml.sample()

@qml.qnode(dev)
def circuit_2():
    qml.Hadamard(wires=0)
    qml.Hadamard(wires=1)
    return qml.sample(wires=[0,2])    # no observable provided and wires specified

>>> print(circuit_1())
[[1, 0, 0],
 [1, 1, 0],
 [1, 0, 0],
 [0, 0, 0],
 [0, 1, 0]]

>>> print(circuit_2())
[[1, 0],
 [1, 0],
 [1, 0],
 [0, 0],
 [0, 0]]

>>> print(qml.draw(circuit_2)())
 0: ──H──╭┤ Sample[basis]
 1: ──H──│┤
 2: ─────╰┤ Sample[basis]

The new qml.apply function can be used to add operations that might have already been instantiated elsewhere to the QNode and other queuing contexts: (#1433)

op = qml.RX(0.4, wires=0)
dev = qml.device("default.qubit", wires=2)

@qml.qnode(dev)
def circuit(x):
    qml.RY(x, wires=0)
    qml.apply(op)
    return qml.expval(qml.PauliZ(0))

>>> print(qml.draw(circuit)(0.6))
0: ──RY(0.6)──RX(0.4)──┤ ⟨Z⟩

Previously instantiated measurements can also be applied to QNodes.

Device Resource Tracker

The new Device Tracker capabilities allows for flexible and versatile tracking of executions, even inside parameter-shift gradients. This functionality will improve the ease of monitoring large batches and remote jobs. (#1355)

dev = qml.device('default.qubit', wires=1, shots=100)

@qml.qnode(dev, diff_method="parameter-shift")
def circuit(x):
    qml.RX(x, wires=0)
    return qml.expval(qml.PauliZ(0))

x = np.array(0.1)

with qml.Tracker(circuit.device) as tracker:
    qml.grad(circuit)(x)

>>> tracker.totals
{'executions': 3, 'shots': 300, 'batches': 1, 'batch_len': 2}
>>> tracker.history
{'executions': [1, 1, 1],
 'shots': [100, 100, 100],
 'batches': [1],
 'batch_len': [2]}
>>> tracker.latest
{'batches': 1, 'batch_len': 2}

Users can also provide a custom function to the callback keyword that gets called each time the information is updated. This functionality allows users to monitor remote jobs or large parameter-shift batches.

>>> def shots_info(totals, history, latest):
...     print("Total shots: ", totals['shots'])
>>> with qml.Tracker(circuit.device, callback=shots_info) as tracker:
...     qml.grad(circuit)(0.1)
Total shots:  100
Total shots:  200
Total shots:  300
Total shots:  300

Containerization support

Docker support for building PennyLane with support for all interfaces (TensorFlow, Torch, and Jax), as well as device plugins and QChem, for GPUs and CPUs, has been added. (#1391)

The build process using Docker and make requires that the repository source code is cloned or downloaded from GitHub. Visit the the detailed description for an extended list of options.

Improved Hamiltonian simulations

Added a sparse Hamiltonian observable and the functionality to support computing its expectation value with default.qubit. (#1398)

For example, the following QNode returns the expectation value of a sparse Hamiltonian:
```
dev = qml.device("default.qubit", wires=2)

@qml.qnode(dev, diff_method="parameter-shift")
def circuit(param, H):
    qml.PauliX(0)
    qml.SingleExcitation(param, wires=[0, 1])
    return qml.expval(qml.SparseHamiltonian(H, [0, 1]))
```
We can execute this QNode, passing in a sparse identity matrix:
```
>>> print(circuit([0.5], scipy.sparse.eye(4).tocoo()))
0.9999999999999999
```
The expectation value of the sparse Hamiltonian is computed directly, which leads to executions that are faster by orders of magnitude. Note that "parameter-shift" is the only differentiation method that is currently supported when the observable is a sparse Hamiltonian.

VQE problems can now be intuitively set up by passing the Hamiltonian as an observable. (#1474)

dev = qml.device("default.qubit", wires=2)
H = qml.Hamiltonian([1., 2., 3.],  [qml.PauliZ(0), qml.PauliY(0), qml.PauliZ(1)])
w = qml.init.strong_ent_layers_uniform(1, 2, seed=1967)

@qml.qnode(dev)
def circuit(w):
    qml.templates.StronglyEntanglingLayers(w, wires=range(2))
    return qml.expval(H)

>>> print(circuit(w))
-1.5133943637878295
>>> print(qml.grad(circuit)(w))
[[[-8.32667268e-17  1.39122955e+00 -9.12462052e-02]
[ 1.02348685e-16 -7.77143238e-01 -1.74708049e-01]]]

Note that other measurement types like var(H) or sample(H), as well as multiple expectations like expval(H1), expval(H2) are not supported.

Added functionality to compute the sparse matrix representation of a qml.Hamiltonian object. (#1394)

New gradients module

A new gradients module qml.gradients has been added, which provides differentiable quantum gradient transforms. (#1476) (#1479) (#1486)

Available quantum gradient transforms include:

qml.gradients.finite_diff
qml.gradients.param_shift
qml.gradients.param_shift_cv

For example,

>>> params = np.array([0.3,0.4,0.5], requires_grad=True)
>>> with qml.tape.JacobianTape() as tape:
...     qml.RX(params[0], wires=0)
...     qml.RY(params[1], wires=0)
...     qml.RX(params[2], wires=0)
...     qml.expval(qml.PauliZ(0))
...     qml.var(qml.PauliZ(0))
>>> tape.trainable_params = {0, 1, 2}
>>> gradient_tapes, fn = qml.gradients.finite_diff(tape)
>>> res = dev.batch_execute(gradient_tapes)
>>> fn(res)
array([[-0.69688381, -0.32648317, -0.68120105],
       [ 0.8788057 ,  0.41171179,  0.85902895]])

Even more new operations and templates

Grover Diffusion Operator template added. (#1442)

For example, if we have an oracle that marks the "all ones" state with a negative sign:

n_wires = 3
wires = list(range(n_wires))

def oracle():
    qml.Hadamard(wires[-1])
    qml.Toffoli(wires=wires)
    qml.Hadamard(wires[-1])

We can perform Grover's Search Algorithm:

dev = qml.device('default.qubit', wires=wires)

@qml.qnode(dev)
def GroverSearch(num_iterations=1):
    for wire in wires:
        qml.Hadamard(wire)

    for _ in range(num_iterations):
        oracle()
        qml.templates.GroverOperator(wires=wires)

    return qml.probs(wires)

We can see this circuit yields the marked state with high probability:

>>> GroverSearch(num_iterations=1)
tensor([0.03125, 0.03125, 0.03125, 0.03125, 0.03125, 0.03125, 0.03125,
        0.78125], requires_grad=True)
>>> GroverSearch(num_iterations=2)
tensor([0.0078125, 0.0078125, 0.0078125, 0.0078125, 0.0078125, 0.0078125,
    0.0078125, 0.9453125], requires_grad=True)

A decomposition has been added to QubitUnitary that makes the single-qubit case fully differentiable in all interfaces. Furthermore, a quantum function transform, unitary_to_rot(), has been added to decompose all single-qubit instances of QubitUnitary in a quantum circuit. (#1427)

Instances of QubitUnitary may now be decomposed directly to Rot operations, or RZ operations if the input matrix is diagonal. For example, let

>>> U = np.array([
    [-0.28829348-0.78829734j,  0.30364367+0.45085995j],
    [ 0.53396245-0.10177564j,  0.76279558-0.35024096j]
])

Then, we can compute the decomposition as:

>>> qml.QubitUnitary.decomposition(U, wires=0)
[Rot(-0.24209530281458358, 1.1493817777199102, 1.733058145303424, wires=[0])]

We can also apply the transform directly to a quantum function, and compute the gradients of parameters used to construct the unitary matrices.

def qfunc_with_qubit_unitary(angles):
    z, x = angles[0], angles[1]

    Z_mat = np.array([[np.exp(-1j * z / 2), 0.0], [0.0, np.exp(1j * z / 2)]])

    c = np.cos(x / 2)
    s = np.sin(x / 2) * 1j
    X_mat = np.array([[c, -s], [-s, c]])

    qml.Hadamard(wires="a")
    qml.QubitUnitary(Z_mat, wires="a")
    qml.QubitUnitary(X_mat, wires="b")
    qml.CNOT(wires=["b", "a"])
    return qml.expval(qml.PauliX(wires="a"))

>>> dev = qml.device("default.qubit", wires=["a", "b"])
>>> transformed_qfunc = qml.transforms.unitary_to_rot(qfunc_with_qubit_unitary)
>>> transformed_qnode = qml.QNode(transformed_qfunc, dev)
>>> input = np.array([0.3, 0.4], requires_grad=True)
>>> transformed_qnode(input)
tensor(0.95533649, requires_grad=True)
>>> qml.grad(transformed_qnode)(input)
array([-0.29552021,  0.        ])

Ising YY gate functionality added. (#1358)

Improvements

The tape does not verify any more that all Observables have owners in the annotated queue. (#1505)

This allows manipulation of Observables inside a tape context. An example is expval(Tensor(qml.PauliX(0), qml.Identity(1)).prune()) which makes the expval an owner of the pruned tensor and its constituent observables, but leaves the original tensor in the queue without an owner.
The step and step_and_cost methods of QNGOptimizer now accept a custom grad_fn keyword argument to use for gradient computations. (#1487)
The precision used by default.qubit.jax now matches the float precision indicated by
```
from jax.config import config
config.read('jax_enable_x64')
```
where True means float64/complex128 and False means float32/complex64. (#1485)
The ./pennylane/ops/qubit.py file is broken up into a folder of six separate files. (#1467)
Changed to using commas as the separator of wires in the string representation of qml.Hamiltonian objects for multi-qubit terms. (#1465)
Changed to using np.object_ instead of np.object as per the NumPy deprecations starting version 1.20. (#1466)
Change the order of the covariance matrix and the vector of means internally in default.gaussian. (#1331)
Added the id attribute to templates. (#1438)
The qml.math module, for framework-agnostic tensor manipulation, has two new functions available: (#1490)
- qml.math.get_trainable_indices(sequence_of_tensors): returns the indices corresponding to trainable tensors in the input sequence.
- qml.math.unwrap(sequence_of_tensors): unwraps a sequence of tensor-like objects to NumPy arrays.
In addition, the behaviour of qml.math.requires_grad has been improved in order to correctly determine trainability during Autograd and JAX backwards passes.

A new tape method, tape.unwrap() is added. This method is a context manager; inside the context, the tape's parameters are unwrapped to NumPy arrays and floats, and the trainable parameter indices are set. (#1491)

These changes are temporary, and reverted on exiting the context.

>>> with tf.GradientTape():
...     with qml.tape.QuantumTape() as tape:
...         qml.RX(tf.Variable(0.1), wires=0)
...         qml.RY(tf.constant(0.2), wires=0)
...         qml.RZ(tf.Variable(0.3), wires=0)
...     with tape.unwrap():
...         print("Trainable params:", tape.trainable_params)
...         print("Unwrapped params:", tape.get_parameters())
Trainable params: {0, 2}
Unwrapped params: [0.1, 0.3]
>>> print("Original parameters:", tape.get_parameters())
Original parameters: [<tf.Variable 'Variable:0' shape=() dtype=float32, numpy=0.1>,
  <tf.Variable 'Variable:0' shape=() dtype=float32, numpy=0.3>]

In addition, qml.tape.Unwrap is a context manager that unwraps multiple tapes:

>>> with qml.tape.Unwrap(tape1, tape2):

Breaking changes

Removed the deprecated tape methods get_resources and get_depth as they are superseded by the specs tape attribute. (#1522)
Specifying shots=None with qml.sample was previously deprecated. From this release onwards, setting shots=None when sampling will raise an error. (#1522)
The existing pennylane.collections.apply function is no longer accessible via qml.apply, and needs to be imported directly from the collections package. (#1358)

Bug fixes

Fixes a bug in qml.adjoint and qml.ctrl where the adjoint of operations outside of a QNode or a QuantumTape could not be obtained. (#1532)
Fixes a bug in GradientDescentOptimizer and NesterovMomentumOptimizer where a cost function with one trainable parameter and non-trainable parameters raised an error. (#1495)
Fixed an example in the documentation's introduction to numpy gradients, where the wires were a non-differentiable argument to the QNode. (#1499)
Fixed a bug where the adjoint of qml.QFT when using the qml.adjoint function was not correctly computed. (#1451)
Fixed the differentiability of the operationIsingYY for Autograd, Jax and Tensorflow. (#1425)
Fixed a bug in the torch interface that prevented gradients from being computed on a GPU. (#1426)
Quantum function transforms now preserve the format of the measurement results, so that a single measurement returns a single value rather than an array with a single element. (#1434)
Fixed a bug in the parameter-shift Hessian implementation, which resulted in the incorrect Hessian being returned for a cost function that performed post-processing on a vector-valued QNode. (#1436)
Fixed a bug in the initialization of QubitUnitary where the size of the matrix was not checked against the number of wires. (#1439)

Documentation

Improved Contribution Guide and Pull Requests Guide. (#1461)
Examples have been added to clarify use of the continuous-variable FockStateVector operation in the multi-mode case. (#1472)

Contributors

This release contains contributions from (in alphabetical order):

Juan Miguel Arrazola, Olivia Di Matteo, Anthony Hayes, Theodor Isacsson, Josh Izaac, Soran Jahangiri, Nathan Killoran, Arshpreet Singh Khangura, Leonhard Kunczik, Christina Lee, Romain Moyard, Lee James O'Riordan, Ashish Panigrahi, Nahum Sá, Maria Schuld, Jay Soni, Antal Száva, David Wierichs.

Release 0.16.0

First class support for quantum kernels

The new qml.kernels module provides basic functionalities for working with quantum kernels as well as post-processing methods to mitigate sampling errors and device noise: (#1102)

num_wires = 6
wires = range(num_wires)
dev = qml.device('default.qubit', wires=wires)

@qml.qnode(dev)
def kernel_circuit(x1, x2):
    qml.templates.AngleEmbedding(x1, wires=wires)
    qml.adjoint(qml.templates.AngleEmbedding)(x2, wires=wires)
    return qml.probs(wires)

kernel = lambda x1, x2: kernel_circuit(x1, x2)[0]
X_train = np.random.random((10, 6))
X_test = np.random.random((5, 6))

# Create symmetric square kernel matrix (for training)
K = qml.kernels.square_kernel_matrix(X_train, kernel)

# Compute kernel between test and training data.
K_test = qml.kernels.kernel_matrix(X_train, X_test, kernel)
K1 = qml.kernels.mitigate_depolarizing_noise(K, num_wires, method='single')

Extract the fourier representation of quantum circuits

PennyLane now has a fourier module, which hosts a growing library of methods that help with investigating the Fourier representation of functions implemented by quantum circuits. The Fourier representation can be used to examine and characterize the expressivity of the quantum circuit. (#1160) (#1378)

For example, one can plot distributions over Fourier series coefficients like this one:

Seamless support for working with the Pauli group

Added functionality for constructing and manipulating the Pauli group (#1181).

The function qml.grouping.pauli_group provides a generator to easily loop over the group, or construct and store it in its entirety. For example, we can construct the single-qubit Pauli group like so:

>>> from pennylane.grouping import pauli_group
>>> pauli_group_1_qubit = list(pauli_group(1))
>>> pauli_group_1_qubit
[Identity(wires=[0]), PauliZ(wires=[0]), PauliX(wires=[0]), PauliY(wires=[0])]

We can multiply together its members at the level of Pauli words using the pauli_mult and pauli_multi_with_phase functions. This can be done on arbitrarily-labeled wires as well, by defining a wire map.

>>> from pennylane.grouping import pauli_group, pauli_mult
>>> wire_map = {'a' : 0, 'b' : 1, 'c' : 2}
>>> pg = list(pauli_group(3, wire_map=wire_map))
>>> pg[3]
PauliZ(wires=['b']) @ PauliZ(wires=['c'])
>>> pg[55]
PauliY(wires=['a']) @ PauliY(wires=['b']) @ PauliZ(wires=['c'])
>>> pauli_mult(pg[3], pg[55], wire_map=wire_map)
PauliY(wires=['a']) @ PauliX(wires=['b'])

Functions for conversion of Pauli observables to strings (and back), are included.

>>> from pennylane.grouping import pauli_word_to_string, string_to_pauli_word
>>> pauli_word_to_string(pg[55], wire_map=wire_map)
'YYZ'
>>> string_to_pauli_word('ZXY', wire_map=wire_map)
PauliZ(wires=['a']) @ PauliX(wires=['b']) @ PauliY(wires=['c'])

Calculation of the matrix representation for arbitrary Paulis and wire maps is now also supported.

>>> from pennylane.grouping import pauli_word_to_matrix
>>> wire_map = {'a' : 0, 'b' : 1}
>>> pauli_word = qml.PauliZ('b')  # corresponds to Pauli 'IZ'
>>> pauli_word_to_matrix(pauli_word, wire_map=wire_map)
array([[ 1.,  0.,  0.,  0.],
       [ 0., -1.,  0., -0.],
       [ 0.,  0.,  1.,  0.],
       [ 0., -0.,  0., -1.]])

New transforms

The qml.specs QNode transform creates a function that returns specifications or details about the QNode, including depth, number of gates, and number of gradient executions required. (#1245)

For example:

dev = qml.device('default.qubit', wires=4)

@qml.qnode(dev, diff_method='parameter-shift')
def circuit(x, y):
    qml.RX(x[0], wires=0)
    qml.Toffoli(wires=(0, 1, 2))
    qml.CRY(x[1], wires=(0, 1))
    qml.Rot(x[2], x[3], y, wires=0)
    return qml.expval(qml.PauliZ(0)), qml.expval(qml.PauliX(1))

We can now use the qml.specs transform to generate a function that returns details and resource information:

>>> x = np.array([0.05, 0.1, 0.2, 0.3], requires_grad=True)
>>> y = np.array(0.4, requires_grad=False)
>>> specs_func = qml.specs(circuit)
>>> specs_func(x, y)
{'gate_sizes': defaultdict(int, {1: 2, 3: 1, 2: 1}),
 'gate_types': defaultdict(int, {'RX': 1, 'Toffoli': 1, 'CRY': 1, 'Rot': 1}),
 'num_operations': 4,
 'num_observables': 2,
 'num_diagonalizing_gates': 1,
 'num_used_wires': 3,
 'depth': 4,
 'num_trainable_params': 4,
 'num_parameter_shift_executions': 11,
 'num_device_wires': 4,
 'device_name': 'default.qubit',
 'diff_method': 'parameter-shift'}

The tape methods get_resources and get_depth are superseded by specs and will be deprecated after one release cycle.

Adds a decorator @qml.qfunc_transform to easily create a transformation that modifies the behaviour of a quantum function. (#1315)

For example, consider the following transform, which scales the parameter of all RX gates by :math:x \rightarrow \sin(a) \sqrt{x}, and the parameters of all RY gates by :math:y \rightarrow \cos(a * b) y:

@qml.qfunc_transform
def my_transform(tape, a, b):
    for op in tape.operations + tape.measurements:
        if op.name == "RX":
            x = op.parameters[0]
            qml.RX(qml.math.sin(a) * qml.math.sqrt(x), wires=op.wires)
        elif op.name == "RY":
            y = op.parameters[0]
            qml.RX(qml.math.cos(a * b) * y, wires=op.wires)
        else:
            op.queue()

We can now apply this transform to any quantum function:

dev = qml.device("default.qubit", wires=2)

def ansatz(x):
    qml.Hadamard(wires=0)
    qml.RX(x[0], wires=0)
    qml.RY(x[1], wires=1)
    qml.CNOT(wires=[0, 1])

@qml.qnode(dev)
def circuit(params, transform_weights):
    qml.RX(0.1, wires=0)

    # apply the transform to the ansatz
    my_transform(*transform_weights)(ansatz)(params)

    return qml.expval(qml.PauliZ(1))

We can print this QNode to show that the qfunc transform is taking place:

>>> x = np.array([0.5, 0.3], requires_grad=True)
>>> transform_weights = np.array([0.1, 0.6], requires_grad=True)
>>> print(qml.draw(circuit)(x, transform_weights))
 0: ──RX(0.1)────H──RX(0.0706)──╭C──┤
 1: ──RX(0.299)─────────────────╰X──┤ ⟨Z⟩

Evaluating the QNode, as well as the derivative, with respect to the gate parameter and the transform weights:

>>> circuit(x, transform_weights)
tensor(0.00672829, requires_grad=True)
>>> qml.grad(circuit)(x, transform_weights)
(array([ 0.00671711, -0.00207359]), array([6.69695008e-02, 3.73694364e-06]))

Adds a hamiltonian_expand tape transform. This takes a tape ending in qml.expval(H), where H is a Hamiltonian, and maps it to a collection of tapes which can be executed and passed into a post-processing function yielding the expectation value. (#1142)

Example use:
```
H = qml.PauliZ(0) + 3 * qml.PauliZ(0) @ qml.PauliX(1)

with qml.tape.QuantumTape() as tape:
    qml.Hadamard(wires=1)
    qml.expval(H)

tapes, fn = qml.transforms.hamiltonian_expand(tape)
```
We can now evaluate the transformed tapes, and apply the post-processing function:
```
>>> dev = qml.device("default.qubit", wires=3)
>>> res = dev.batch_execute(tapes)
>>> fn(res)
3.999999999999999
```

The quantum_monte_carlo transform has been added, allowing an input circuit to be transformed into the full quantum Monte Carlo algorithm. (#1316)

Suppose we want to measure the expectation value of the sine squared function according to a standard normal distribution. We can calculate the expectation value analytically as 0.432332, but we can also estimate using the quantum Monte Carlo algorithm. The first step is to discretize the problem:

from scipy.stats import norm

m = 5
M = 2 ** m

xmax = np.pi  # bound to region [-pi, pi]
xs = np.linspace(-xmax, xmax, M)

probs = np.array([norm().pdf(x) for x in xs])
probs /= np.sum(probs)

func = lambda i: np.sin(xs[i]) ** 2
r_rotations = np.array([2 * np.arcsin(np.sqrt(func(i))) for i in range(M)])

The quantum_monte_carlo transform can then be used:

from pennylane.templates.state_preparations.mottonen import (
    _uniform_rotation_dagger as r_unitary,
)

n = 6
N = 2 ** n

a_wires = range(m)
wires = range(m + 1)
target_wire = m
estimation_wires = range(m + 1, n + m + 1)

dev = qml.device("default.qubit", wires=(n + m + 1))

def fn():
    qml.templates.MottonenStatePreparation(np.sqrt(probs), wires=a_wires)
    r_unitary(qml.RY, r_rotations, control_wires=a_wires[::-1], target_wire=target_wire)

@qml.qnode(dev)
def qmc():
    qml.quantum_monte_carlo(fn, wires, target_wire, estimation_wires)()
    return qml.probs(estimation_wires)

phase_estimated = np.argmax(qmc()[:int(N / 2)]) / N

The estimated value can be retrieved using:

>>> (1 - np.cos(np.pi * phase_estimated)) / 2
0.42663476277231915

The resources required to perform the quantum Monte Carlo algorithm can also be inspected using the specs transform.

Extended QAOA module

Functionality to support solving the maximum-weighted cycle problem has been added to the qaoa module. (#1207) (#1209) (#1251) (#1213) (#1220) (#1214) (#1283) (#1297) (#1396) (#1403)

The max_weight_cycle function returns the appropriate cost and mixer Hamiltonians:

>>> a = np.random.random((3, 3))
>>> np.fill_diagonal(a, 0)
>>> g = nx.DiGraph(a)  # create a random directed graph
>>> cost, mixer, mapping = qml.qaoa.max_weight_cycle(g)
>>> print(cost)
  (-0.9775906842165344) [Z2]
+ (-0.9027248603361988) [Z3]
+ (-0.8722207409852838) [Z0]
+ (-0.6426184210832898) [Z5]
+ (-0.2832594164291379) [Z1]
+ (-0.0778133996933755) [Z4]
>>> print(mapping)
{0: (0, 1), 1: (0, 2), 2: (1, 0), 3: (1, 2), 4: (2, 0), 5: (2, 1)}

Additional functionality can be found in the qml.qaoa.cycle module.

Extended operations and templates

Added functionality to compute the sparse matrix representation of a qml.Hamiltonian object. (#1394)

coeffs = [1, -0.45]
obs = [qml.PauliZ(0) @ qml.PauliZ(1), qml.PauliY(0) @ qml.PauliZ(1)]
H = qml.Hamiltonian(coeffs, obs)
H_sparse = qml.utils.sparse_hamiltonian(H)

The resulting matrix is a sparse matrix in scipy coordinate list (COO) format:

>>> H_sparse
<4x4 sparse matrix of type '<class 'numpy.complex128'>'
    with 8 stored elements in COOrdinate format>

The sparse matrix can be converted to an array as:

>>> H_sparse.toarray()
array([[ 1.+0.j  ,  0.+0.j  ,  0.+0.45j,  0.+0.j  ],
       [ 0.+0.j  , -1.+0.j  ,  0.+0.j  ,  0.-0.45j],
       [ 0.-0.45j,  0.+0.j  , -1.+0.j  ,  0.+0.j  ],
       [ 0.+0.j  ,  0.+0.45j,  0.+0.j  ,  1.+0.j  ]])

Adds the new template AllSinglesDoubles to prepare quantum states of molecules using the SingleExcitation and DoubleExcitation operations. The new template reduces significantly the number of operations and the depth of the quantum circuit with respect to the traditional UCCSD unitary. (#1383)

For example, consider the case of two particles and four qubits. First, we define the Hartree-Fock initial state and generate all possible single and double excitations.

import pennylane as qml
from pennylane import numpy as np

electrons = 2
qubits = 4

hf_state = qml.qchem.hf_state(electrons, qubits)
singles, doubles = qml.qchem.excitations(electrons, qubits)

Now we can use the template AllSinglesDoubles to define the quantum circuit,

from pennylane.templates import AllSinglesDoubles

wires = range(qubits)

dev = qml.device('default.qubit', wires=wires)

@qml.qnode(dev)
def circuit(weights, hf_state, singles, doubles):
    AllSinglesDoubles(weights, wires, hf_state, singles, doubles)
    return qml.expval(qml.PauliZ(0))

params = np.random.normal(0, np.pi, len(singles) + len(doubles))

and execute it:

>>> circuit(params, hf_state, singles=singles, doubles=doubles)
tensor(-0.73772194, requires_grad=True)

Adds QubitCarry and QubitSum operations for basic arithmetic. (#1169)

The following example adds two 1-bit numbers, returning a 2-bit answer:

dev = qml.device('default.qubit', wires = 4)
a = 0
b = 1

@qml.qnode(dev)
def circuit():
    qml.BasisState(np.array([a, b]), wires=[1, 2])
    qml.QubitCarry(wires=[0, 1, 2, 3])
    qml.CNOT(wires=[1, 2])
    qml.QubitSum(wires=[0, 1, 2])
    return qml.probs(wires=[3, 2])

probs = circuit()
bitstrings = tuple(itertools.product([0, 1], repeat = 2))
indx = np.argwhere(probs == 1).flatten()[0]
output = bitstrings[indx]

>>> print(output)
(0, 1)

Added the qml.Projector observable, which is available on all devices inheriting from the QubitDevice class. (#1356) (#1368)

Using qml.Projector, we can define the basis state projectors to use when computing expectation values. Let us take for example a circuit that prepares Bell states:
```
dev = qml.device("default.qubit", wires=2)

@qml.qnode(dev)
def circuit(basis_state):
    qml.Hadamard(wires=[0])
    qml.CNOT(wires=[0, 1])
    return qml.expval(qml.Projector(basis_state, wires=[0, 1]))
```
We can then specify the |00> basis state to construct the |00><00| projector and compute the expectation value:
```
>>> basis_state = [0, 0]
>>> circuit(basis_state)
tensor(0.5, requires_grad=True)
```
As expected, we get similar results when specifying the |11> basis state:
```
>>> basis_state = [1, 1]
>>> circuit(basis_state)
tensor(0.5, requires_grad=True)
```
The following new operations have been added:
- The IsingXX gate qml.IsingXX (#1194)
- The IsingZZ gate qml.IsingZZ (#1199)
- The ISWAP gate qml.ISWAP (#1298)
- The reset error noise channel qml.ResetError (#1321)

Improvements

The argnum keyword argument can now be specified for a QNode to define a subset of trainable parameters used to estimate the Jacobian. (#1371)

For example, consider two trainable parameters and a quantum function:

dev = qml.device("default.qubit", wires=2)

x = np.array(0.543, requires_grad=True)
y = np.array(-0.654, requires_grad=True)

def circuit(x,y):
    qml.RX(x, wires=[0])
    qml.RY(y, wires=[1])
    qml.CNOT(wires=[0, 1])
    return qml.expval(qml.PauliZ(0) @ qml.PauliX(1))

When computing the gradient of the QNode, we can specify the trainable parameters to consider by passing the argnum keyword argument:

>>> qnode1 = qml.QNode(circuit, dev, diff_method="parameter-shift", argnum=[0,1])
>>> print(qml.grad(qnode1)(x,y))
(array(0.31434679), array(0.67949903))

Specifying a proper subset of the trainable parameters will estimate the Jacobian:

>>> qnode2 = qml.QNode(circuit, dev, diff_method="parameter-shift", argnum=[0])
>>> print(qml.grad(qnode2)(x,y))
(array(0.31434679), array(0.))

Allows creating differentiable observables that return custom objects such that the observable is supported by devices. (1291)

As an example, first we define NewObservable class:

from pennylane.devices import DefaultQubit

class NewObservable(qml.operation.Observable):
    """NewObservable"""

    num_wires = qml.operation.AnyWires
    num_params = 0
    par_domain = None

    def diagonalizing_gates(self):
        """Diagonalizing gates"""
        return []

Once we have this new observable class, we define a SpecialObject class that can be used to encode data in an observable and a new device that supports our new observable and returns a SpecialObject as the expectation value (the code is shortened for brevity, the extended example can be found as a test in the previously referenced pull request):

class SpecialObject:

    def __init__(self, val):
        self.val = val

    def __mul__(self, other):
        new = SpecialObject(self.val)
        new *= other
        return new

    ...

class DeviceSupportingNewObservable(DefaultQubit):
    name = "Device supporting NewObservable"
    short_name = "default.qubit.newobservable"
    observables = DefaultQubit.observables.union({"NewObservable"})

    def expval(self, observable, **kwargs):
        if self.shots is None and isinstance(observable, NewObservable):
            val = super().expval(qml.PauliZ(wires=0), **kwargs)
            return SpecialObject(val)

        return super().expval(observable, **kwargs)

At this point, we can create a device that will support the differentiation of a NewObservable object:

dev = DeviceSupportingNewObservable(wires=1, shots=None)

@qml.qnode(dev, diff_method="parameter-shift")
def qnode(x):
    qml.RY(x, wires=0)
    return qml.expval(NewObservable(wires=0))

We can then compute the jacobian of this object:

>>> result = qml.jacobian(qnode)(0.2)
>>> print(result)
<__main__.SpecialObject object at 0x7fd2c54721f0>
>>> print(result.item().val)
-0.19866933079506116

PennyLane NumPy now includes the random module's Generator objects, the recommended way of random number generation. This allows for random number generation using a local, rather than global seed. (#1267)
```
from pennylane import numpy as np

rng = np.random.default_rng()
random_mat1 = rng.random((3,2))
random_mat2 = rng.standard_normal(3, requires_grad=False)
```
The performance of adjoint jacobian differentiation was significantly improved as the method now reuses the state computed on the forward pass. This can be turned off to save memory with the Torch and TensorFlow interfaces by passing adjoint_cache=False during QNode creation. (#1341)
The Operator (and by inheritance, the Operation and Observable class and their children) now have an id attribute, which can mark an operator in a circuit, for example to identify it on the tape by a tape transform. (#1377)
The benchmark module was deleted, since it was outdated and is superseded by the new separate benchmark repository. (#1343)

Decompositions in terms of elementary gates has been added for:

qml.CSWAP (#1306)
qml.SWAP (#1329)
qml.SingleExcitation (#1303)
qml.SingleExcitationPlus and qml.SingleExcitationMinus (#1278)
qml.DoubleExcitation (#1303)
qml.Toffoli (#1320)

qml.MultiControlledX. (#1287) When controlling on three or more wires, an ancilla register of worker wires is required to support the decomposition.

ctrl_wires = [f"c{i}" for i in range(5)]
work_wires = [f"w{i}" for i in range(3)]
target_wires = ["t0"]
all_wires = ctrl_wires + work_wires + target_wires

dev = qml.device("default.qubit", wires=all_wires)

with qml.tape.QuantumTape() as tape:
    qml.MultiControlledX(control_wires=ctrl_wires, wires=target_wires, work_wires=work_wires)

>>> tape = tape.expand(depth=1)
>>> print(tape.draw(wire_order=qml.wires.Wires(all_wires)))

 c0: ──────────────╭C──────────────────────╭C──────────┤
 c1: ──────────────├C──────────────────────├C──────────┤
 c2: ──────────╭C──│───╭C──────────────╭C──│───╭C──────┤
 c3: ──────╭C──│───│───│───╭C──────╭C──│───│───│───╭C──┤
 c4: ──╭C──│───│───│───│───│───╭C──│───│───│───│───│───┤
 w0: ──│───│───├C──╰X──├C──│───│───│───├C──╰X──├C──│───┤
 w1: ──│───├C──╰X──────╰X──├C──│───├C──╰X──────╰X──├C──┤
 w2: ──├C──╰X──────────────╰X──├C──╰X──────────────╰X──┤
 t0: ──╰X──────────────────────╰X──────────────────────┤

Added qml.CPhase as an alias for the existing qml.ControlledPhaseShift operation. (#1319).
The Device class now uses caching when mapping wires. (#1270)
The Wires class now uses caching for computing its hash. (#1270)
Added custom gate application for Toffoli in default.qubit. (#1249)
Added validation for noise channel parameters. Invalid noise parameters now raise a ValueError. (#1357)
The device test suite now provides test cases for checking gates by comparing expectation values. (#1212)
PennyLane's test suite is now code-formatted using black -l 100. (#1222)
PennyLane's qchem package and tests are now code-formatted using black -l 100. (#1311)

Breaking changes

The qml.inv() function is now deprecated with a warning to use the more general qml.adjoint(). (#1325)
Removes support for Python 3.6 and adds support for Python 3.9. (#1228)
The tape methods get_resources and get_depth are superseded by specs and will be deprecated after one release cycle. (#1245)
Using the qml.sample() measurement on devices with shots=None continue to raise a warning with this functionality being fully deprecated and raising an error after one release cycle. (#1079) (#1196)

Bug fixes

QNodes now display readable information when in interactive environments or when printed. (#1359).
Fixes a bug with qml.math.cast where the MottonenStatePreparation operation expected a float type instead of double. (#1400)
Fixes a bug where a copy of qml.ControlledQubitUnitary was non-functional as it did not have all the necessary information. (#1411)
Warns when adjoint or reversible differentiation specified or called on a device with finite shots. (#1406)
Fixes the differentiability of the operations IsingXX and IsingZZ for Autograd, Jax and Tensorflow. (#1390)
Fixes a bug where multiple identical Hamiltonian terms will produce a different result with optimize=True using ExpvalCost. (#1405)
Fixes bug where shots=None was not reset when changing shots temporarily in a QNode call like circuit(0.1, shots=3). (#1392)
Fixes floating point errors with diff_method="finite-diff" and order=1 when parameters are float32. (#1381)
Fixes a bug where qml.ctrl would fail to transform gates that had no control defined and no decomposition defined. (#1376)
Copying the JacobianTape now correctly also copies the jacobian_options attribute. This fixes a bug allowing the JAX interface to support adjoint differentiation. (#1349)
Fixes drawing QNodes that contain multiple measurements on a single wire. (#1353)
Fixes drawing QNodes with no operations. (#1354)
Fixes incorrect wires in the decomposition of the ControlledPhaseShift operation. (#1338)
Fixed tests for the Permute operation that used a QNode and hence expanded tapes twice instead of once due to QNode tape expansion and an explicit tape expansion call. (#1318).
Prevent Hamiltonians that share wires from being multiplied together. (#1273)
Fixed a bug where the custom range sequences could not be passed to the StronglyEntanglingLayers template. (#1332)
Fixed a bug where qml.sum() and qml.dot() do not support the JAX interface. (#1380)

Documentation

Math present in the QubitParamShiftTape class docstring now renders correctly. (#1402)
Fix typo in the documentation of qml.StronglyEntanglingLayers. (#1367)
Fixed typo in TensorFlow interface documentation (#1312)
Fixed typos in the mathematical expressions in documentation of qml.DoubleExcitation. (#1278)
Remove unsupported None option from the qml.QNode docstrings. (#1271)
Updated the docstring of qml.PolyXP to reference the new location of internal usage. (#1262)
Removes occurrences of the deprecated device argument analytic from the documentation. (#1261)
Updated PyTorch and TensorFlow interface introductions. (#1333)
Updates the quantum chemistry quickstart to reflect recent changes to the qchem module. (#1227)

Contributors

This release contains contributions from (in alphabetical order):

Marius Aglitoiu, Vishnu Ajith, Juan Miguel Arrazola, Thomas Bromley, Jack Ceroni, Alaric Cheng, Miruna Daian, Olivia Di Matteo, Tanya Garg, Christian Gogolin, Alain Delgado Gran, Diego Guala, Anthony Hayes, Ryan Hill, Theodor Isacsson, Josh Izaac, Soran Jahangiri, Pavan Jayasinha, Nathan Killoran, Christina Lee, Ryan Levy, Alberto Maldonado, Johannes Jakob Meyer, Romain Moyard, Ashish Panigrahi, Nahum Sá, Maria Schuld, Brian Shi, Antal Száva, David Wierichs, Vincent Wong.

Release 0.15.1

Bug fixes

Fixes two bugs in the parameter-shift Hessian. (#1260)
- Fixes a bug where having an unused parameter in the Autograd interface would result in an indexing error during backpropagation.
- The parameter-shift Hessian only supports the two-term parameter-shift rule currently, so raises an error if asked to differentiate any unsupported gates (such as the controlled rotation gates).
A bug which resulted in qml.adjoint() and qml.inv() failing to work with templates has been fixed. (#1243)
Deprecation warning instances in PennyLane have been changed to UserWarning, to account for recent changes to how Python warnings are filtered in PEP565. (#1211)

Documentation

Updated the order of the parameters to the GaussianState operation to match the way that the PennyLane-SF plugin uses them. (#1255)

Contributors

This release contains contributions from (in alphabetical order):

Thomas Bromley, Olivia Di Matteo, Diego Guala, Anthony Hayes, Ryan Hill, Josh Izaac, Christina Lee, Maria Schuld, Antal Száva.

Release 0.15.0

New features since last release

Better and more flexible shot control

Adds a new optimizer qml.ShotAdaptiveOptimizer, a gradient-descent optimizer where the shot rate is adaptively calculated using the variances of the parameter-shift gradient. (#1139)

By keeping a running average of the parameter-shift gradient and the variance of the parameter-shift gradient, this optimizer frugally distributes a shot budget across the partial derivatives of each parameter.

In addition, if computing the expectation value of a Hamiltonian, weighted random sampling can be used to further distribute the shot budget across the local terms from which the Hamiltonian is constructed.

This optimizer is based on both the iCANS1 and Rosalin shot-adaptive optimizers.

Once constructed, the cost function can be passed directly to the optimizer's step method. The attribute opt.total_shots_used can be used to track the number of shots per iteration.

>>> coeffs = [2, 4, -1, 5, 2]
>>> obs = [
...   qml.PauliX(1),
...   qml.PauliZ(1),
...   qml.PauliX(0) @ qml.PauliX(1),
...   qml.PauliY(0) @ qml.PauliY(1),
...   qml.PauliZ(0) @ qml.PauliZ(1)
... ]
>>> H = qml.Hamiltonian(coeffs, obs)
>>> dev = qml.device("default.qubit", wires=2, shots=100)
>>> cost = qml.ExpvalCost(qml.templates.StronglyEntanglingLayers, H, dev)
>>> params = qml.init.strong_ent_layers_uniform(n_layers=2, n_wires=2)
>>> opt = qml.ShotAdaptiveOptimizer(min_shots=10)
>>> for i in range(5):
...    params = opt.step(cost, params)
...    print(f"Step {i}: cost = {cost(params):.2f}, shots_used = {opt.total_shots_used}")
Step 0: cost = -5.68, shots_used = 240
Step 1: cost = -2.98, shots_used = 336
Step 2: cost = -4.97, shots_used = 624
Step 3: cost = -5.53, shots_used = 1054
Step 4: cost = -6.50, shots_used = 1798

Batches of shots can now be specified as a list, allowing measurement statistics to be course-grained with a single QNode evaluation. (#1103)
```
>>> shots_list = [5, 10, 1000]
>>> dev = qml.device("default.qubit", wires=2, shots=shots_list)
```
When QNodes are executed on this device, a single execution of 1015 shots will be submitted. However, three sets of measurement statistics will be returned; using the first 5 shots, second set of 10 shots, and final 1000 shots, separately.

For example, executing a circuit with two outputs will lead to a result of shape (3, 2):
```
>>> @qml.qnode(dev)
... def circuit(x):
...     qml.RX(x, wires=0)
...     qml.CNOT(wires=[0, 1])
...     return qml.expval(qml.PauliZ(0) @ qml.PauliX(1)), qml.expval(qml.PauliZ(0))
>>> circuit(0.5)
[[0.33333333 1.        ]
 [0.2        1.        ]
 [0.012      0.868     ]]
```
This output remains fully differentiable.

The number of shots can now be specified on a per-call basis when evaluating a QNode. (#1075).

For this, the qnode should be called with an additional shots keyword argument:

>>> dev = qml.device('default.qubit', wires=1, shots=10) # default is 10
>>> @qml.qnode(dev)
... def circuit(a):
...     qml.RX(a, wires=0)
...     return qml.sample(qml.PauliZ(wires=0))
>>> circuit(0.8)
[ 1  1  1 -1 -1  1  1  1  1  1]
>>> circuit(0.8, shots=3)
[ 1  1  1]
>>> circuit(0.8)
[ 1  1  1 -1 -1  1  1  1  1  1]

New differentiable quantum transforms

A new module is available, qml.transforms, which contains differentiable quantum transforms. These are functions that act on QNodes, quantum functions, devices, and tapes, transforming them while remaining fully differentiable.

A new adjoint transform has been added. (#1111) (#1135)

This new method allows users to apply the adjoint of an arbitrary sequence of operations.

def subroutine(wire):
    qml.RX(0.123, wires=wire)
    qml.RY(0.456, wires=wire)

dev = qml.device('default.qubit', wires=1)
@qml.qnode(dev)
def circuit():
    subroutine(0)
    qml.adjoint(subroutine)(0)
    return qml.expval(qml.PauliZ(0))

This creates the following circuit:

>>> print(qml.draw(circuit)())
0: --RX(0.123)--RY(0.456)--RY(-0.456)--RX(-0.123)--| <Z>

Directly applying to a gate also works as expected.

qml.adjoint(qml.RX)(0.123, wires=0) # applies RX(-0.123)

A new transform qml.ctrl is now available that adds control wires to subroutines. (#1157)

def my_ansatz(params):
   qml.RX(params[0], wires=0)
   qml.RZ(params[1], wires=1)

# Create a new operation that applies `my_ansatz`
# controlled by the "2" wire.
my_ansatz2 = qml.ctrl(my_ansatz, control=2)

@qml.qnode(dev)
def circuit(params):
    my_ansatz2(params)
    return qml.state()

This is equivalent to:

@qml.qnode(...)
def circuit(params):
    qml.CRX(params[0], wires=[2, 0])
    qml.CRZ(params[1], wires=[2, 1])
    return qml.state()

The qml.transforms.classical_jacobian transform has been added. (#1186)

This transform returns a function to extract the Jacobian matrix of the classical part of a QNode, allowing the classical dependence between the QNode arguments and the quantum gate arguments to be extracted.

For example, given the following QNode:
```
>>> @qml.qnode(dev)
... def circuit(weights):
...     qml.RX(weights[0], wires=0)
...     qml.RY(weights[0], wires=1)
...     qml.RZ(weights[2] ** 2, wires=1)
...     return qml.expval(qml.PauliZ(0))
```
We can use this transform to extract the relationship :math:f: \mathbb{R}^n \rightarrow\mathbb{R}^m between the input QNode arguments :math:w and the gate arguments :math:g, for a given value of the QNode arguments:
```
>>> cjac_fn = qml.transforms.classical_jacobian(circuit)
>>> weights = np.array([1., 1., 1.], requires_grad=True)
>>> cjac = cjac_fn(weights)
>>> print(cjac)
[[1. 0. 0.]
 [1. 0. 0.]
 [0. 0. 2.]]
```
The returned Jacobian has rows corresponding to gate arguments, and columns corresponding to QNode arguments; that is, :math:J_{ij} = \frac{\partial}{\partial g_i} f(w_j).

More operations and templates

Added the SingleExcitation two-qubit operation, which is useful for quantum chemistry applications. (#1121)

It can be used to perform an SO(2) rotation in the subspace spanned by the states :math:|01\rangle and :math:|10\rangle. For example, the following circuit performs the transformation :math:|10\rangle \rightarrow \cos(\phi/2)|10\rangle - \sin(\phi/2)|01\rangle:
```
dev = qml.device('default.qubit', wires=2)

@qml.qnode(dev)
def circuit(phi):
    qml.PauliX(wires=0)
    qml.SingleExcitation(phi, wires=[0, 1])
```
The SingleExcitation operation supports analytic gradients on hardware using only four expectation value calculations, following results from Kottmann et al.
Added the DoubleExcitation four-qubit operation, which is useful for quantum chemistry applications. (#1123)

It can be used to perform an SO(2) rotation in the subspace spanned by the states :math:|1100\rangle and :math:|0011\rangle. For example, the following circuit performs the transformation :math:|1100\rangle\rightarrow \cos(\phi/2)|1100\rangle - \sin(\phi/2)|0011\rangle:
```
dev = qml.device('default.qubit', wires=2)

@qml.qnode(dev)
def circuit(phi):
    qml.PauliX(wires=0)
    qml.PauliX(wires=1)
    qml.DoubleExcitation(phi, wires=[0, 1, 2, 3])
```
The DoubleExcitation operation supports analytic gradients on hardware using only four expectation value calculations, following results from Kottmann et al..

Added the QuantumMonteCarlo template for performing quantum Monte Carlo estimation of an expectation value on simulator. (#1130)

The following example shows how the expectation value of sine squared over a standard normal distribution can be approximated:

from scipy.stats import norm

m = 5
M = 2 ** m
n = 10
N = 2 ** n
target_wires = range(m + 1)
estimation_wires = range(m + 1, n + m + 1)

xmax = np.pi  # bound to region [-pi, pi]
xs = np.linspace(-xmax, xmax, M)

probs = np.array([norm().pdf(x) for x in xs])
probs /= np.sum(probs)

func = lambda i: np.sin(xs[i]) ** 2

dev = qml.device("default.qubit", wires=(n + m + 1))

@qml.qnode(dev)
def circuit():
    qml.templates.QuantumMonteCarlo(
        probs,
        func,
        target_wires=target_wires,
        estimation_wires=estimation_wires,
    )
    return qml.probs(estimation_wires)

phase_estimated = np.argmax(circuit()[:int(N / 2)]) / N
expectation_estimated = (1 - np.cos(np.pi * phase_estimated)) / 2

Added the QuantumPhaseEstimation template for performing quantum phase estimation for an input unitary matrix. (#1095)

Consider the matrix corresponding to a rotation from an RX gate:

>>> phase = 5
>>> target_wires = [0]
>>> unitary = qml.RX(phase, wires=0).matrix

The phase parameter can be estimated using QuantumPhaseEstimation. For example, using five phase-estimation qubits:

n_estimation_wires = 5
estimation_wires = range(1, n_estimation_wires + 1)

dev = qml.device("default.qubit", wires=n_estimation_wires + 1)

@qml.qnode(dev)
def circuit():
    # Start in the |+> eigenstate of the unitary
    qml.Hadamard(wires=target_wires)

    QuantumPhaseEstimation(
        unitary,
        target_wires=target_wires,
        estimation_wires=estimation_wires,
    )

    return qml.probs(estimation_wires)

phase_estimated = np.argmax(circuit()) / 2 ** n_estimation_wires

# Need to rescale phase due to convention of RX gate
phase_estimated = 4 * np.pi * (1 - phase)

Added the ControlledPhaseShift gate as well as the QFT operation for applying quantum Fourier transforms. (#1064)

@qml.qnode(dev)
def circuit_qft(basis_state):
    qml.BasisState(basis_state, wires=range(3))
    qml.templates.QFT(wires=range(3))
    return qml.state()

Added the ControlledQubitUnitary operation. This enables implementation of multi-qubit gates with a variable number of control qubits. It is also possible to specify a different state for the control qubits using the control_values argument (also known as a mixed-polarity multi-controlled operation). (#1069) (#1104)

For example, we can create a multi-controlled T gate using:
```
T = qml.T._matrix()
qml.ControlledQubitUnitary(T, control_wires=[0, 1, 3], wires=2, control_values="110")
```
Here, the T gate will be applied to wire 2 if control wires 0 and 1 are in state 1, and control wire 3 is in state 0. If no value is passed to control_values, the gate will be applied if all control wires are in the 1 state.
Added MultiControlledX for multi-controlled NOT gates. This is a special case of ControlledQubitUnitary that applies a Pauli X gate conditioned on the state of an arbitrary number of control qubits. (#1104)

Support for higher-order derivatives on hardware

Computing second derivatives and Hessians of QNodes is now supported with the parameter-shift differentiation method, on all machine learning interfaces. (#1130) (#1129) (#1110)

Hessians are computed using the parameter-shift rule, and can be evaluated on both hardware and simulator devices.

dev = qml.device('default.qubit', wires=1)

@qml.qnode(dev, diff_method="parameter-shift")
def circuit(p):
    qml.RY(p[0], wires=0)
    qml.RX(p[1], wires=0)
    return qml.expval(qml.PauliZ(0))

x = np.array([1.0, 2.0], requires_grad=True)

>>> hessian_fn = qml.jacobian(qml.grad(circuit))
>>> hessian_fn(x)
[[0.2248451 0.7651474]
 [0.7651474 0.2248451]]

Added the function finite_diff() to compute finite-difference approximations to the gradient and the second-order derivatives of arbitrary callable functions. (#1090)

This is useful to compute the derivative of parametrized pennylane.Hamiltonian observables with respect to their parameters.

For example, in quantum chemistry simulations it can be used to evaluate the derivatives of the electronic Hamiltonian with respect to the nuclear coordinates:
```
>>> def H(x):
...    return qml.qchem.molecular_hamiltonian(['H', 'H'], x)[0]
>>> x = np.array([0., 0., -0.66140414, 0., 0., 0.66140414])
>>> grad_fn = qml.finite_diff(H, N=1)
>>> grad = grad_fn(x)
>>> deriv2_fn = qml.finite_diff(H, N=2, idx=[0, 1])
>>> deriv2_fn(x)
```
The JAX interface now supports all devices, including hardware devices, via the parameter-shift differentiation method. (#1076)

For example, using the JAX interface with Cirq:
```
dev = qml.device('cirq.simulator', wires=1)
@qml.qnode(dev, interface="jax", diff_method="parameter-shift")
def circuit(x):
    qml.RX(x[1], wires=0)
    qml.Rot(x[0], x[1], x[2], wires=0)
    return qml.expval(qml.PauliZ(0))
weights = jnp.array([0.2, 0.5, 0.1])
print(circuit(weights))
```
Currently, when used with the parameter-shift differentiation method, only a single returned expectation value or variance is supported. Multiple expectations/variances, as well as probability and state returns, are not currently allowed.

Improvements

dev = qml.device("default.qubit", wires=2)

inputstate = [np.sqrt(0.2), np.sqrt(0.3), np.sqrt(0.4), np.sqrt(0.1)]

@qml.qnode(dev)
def circuit():
    mottonen.MottonenStatePreparation(inputstate,wires=[0, 1])
    return qml.expval(qml.PauliZ(0))

Previously returned:

>>> print(qml.draw(circuit)())
0: ──RY(1.57)──╭C─────────────╭C──╭C──╭C──┤ ⟨Z⟩
1: ──RY(1.35)──╰X──RY(0.422)──╰X──╰X──╰X──┤

In this release, it now returns:

>>> print(qml.draw(circuit)())
0: ──RY(1.57)──╭C─────────────╭C──┤ ⟨Z⟩
1: ──RY(1.35)──╰X──RY(0.422)──╰X──┤

The templates are now classes inheriting from Operation, and define the ansatz in their expand() method. This change does not affect the user interface. (#1138) (#1156) (#1163) (#1192)

For convenience, some templates have a new method that returns the expected shape of the trainable parameter tensor, which can be used to create random tensors.
```
shape = qml.templates.BasicEntanglerLayers.shape(n_layers=2, n_wires=4)
weights = np.random.random(shape)
qml.templates.BasicEntanglerLayers(weights, wires=range(4))
```
QubitUnitary now validates to ensure the input matrix is two dimensional. (#1128)

Most layers in Pytorch or Keras accept arbitrary dimension inputs, where each dimension barring the last (in the case where the actual weight function of the layer operates on one-dimensional vectors) is broadcast over. This is now also supported by KerasLayer and TorchLayer. (#1062).

Example use:

dev = qml.device("default.qubit", wires=4)
x = tf.ones((5, 4, 4))

@qml.qnode(dev)
def layer(weights, inputs):
    qml.templates.AngleEmbedding(inputs, wires=range(4))
    qml.templates.StronglyEntanglingLayers(weights, wires=range(4))
    return [qml.expval(qml.PauliZ(i)) for i in range(4)]

qlayer = qml.qnn.KerasLayer(layer, {"weights": (4, 4, 3)}, output_dim=4)
out = qlayer(x)

The output tensor has the following shape:

>>> out.shape
(5, 4, 4)

If only one argument to the function qml.grad has the requires_grad attribute set to True, then the returned gradient will be a NumPy array, rather than a tuple of length 1. (#1067) (#1081)
An improvement has been made to how QubitDevice generates and post-processess samples, allowing QNode measurement statistics to work on devices with more than 32 qubits. (#1088)
Due to the addition of density_matrix() as a return type from a QNode, tuples are now supported by the output_dim parameter in qnn.KerasLayer. (#1070)
Two new utility methods are provided for working with quantum tapes. (#1175)
- qml.tape.get_active_tape() gets the currently recording tape.
- tape.stop_recording() is a context manager that temporarily stops the currently recording tape from recording additional tapes or quantum operations.
For example:
```
>>> with qml.tape.QuantumTape():
...     qml.RX(0, wires=0)
...     current_tape = qml.tape.get_active_tape()
...     with current_tape.stop_recording():
...         qml.RY(1.0, wires=1)
...     qml.RZ(2, wires=1)
>>> current_tape.operations
[RX(0, wires=[0]), RZ(2, wires=[1])]
```
When printing qml.Hamiltonian objects, the terms are sorted by number of wires followed by coefficients. (#981)
Adds qml.math.conj to the PennyLane math module. (#1143)

This new method will do elementwise conjugation to the given tensor-like object, correctly dispatching to the required tensor-manipulation framework to preserve differentiability.
```
>>> a = np.array([1.0 + 2.0j])
>>> qml.math.conj(a)
array([1.0 - 2.0j])
```
The four-term parameter-shift rule, as used by the controlled rotation operations, has been updated to use coefficients that minimize the variance as per https://arxiv.org/abs/2104.05695. (#1206)
A new transform qml.transforms.invisible has been added, to make it easier to transform QNodes. (#1175)

Breaking changes

Devices do not have an analytic argument or attribute anymore. Instead, shots is the source of truth for whether a simulator estimates return values from a finite number of shots, or whether it returns analytic results (shots=None). (#1079) (#1196)
```
dev_analytic = qml.device('default.qubit', wires=1, shots=None)
dev_finite_shots = qml.device('default.qubit', wires=1, shots=1000)

def circuit():
    qml.Hadamard(wires=0)
    return qml.expval(qml.PauliZ(wires=0))

circuit_analytic = qml.QNode(circuit, dev_analytic)
circuit_finite_shots = qml.QNode(circuit, dev_finite_shots)
```
Devices with shots=None return deterministic, exact results:
```
>>> circuit_analytic()
0.0
>>> circuit_analytic()
0.0
```
Devices with shots > 0 return stochastic results estimated from samples in each run:
```
>>> circuit_finite_shots()
-0.062
>>> circuit_finite_shots()
0.034
```
The qml.sample() measurement can only be used on devices on which the number of shots is set explicitly.
If creating a QNode from a quantum function with an argument named shots, a UserWarning is raised, warning the user that this is a reserved argument to change the number of shots on a per-call basis. (#1075)
For devices inheriting from QubitDevice, the methods expval, var, sample accept two new keyword arguments --- shot_range and bin_size. (#1103)

These new arguments allow for the statistics to be performed on only a subset of device samples. This finer level of control is accessible from the main UI by instantiating a device with a batch of shots.

For example, consider the following device:
```
>>> dev = qml.device("my_device", shots=[5, (10, 3), 100])
```
This device will execute QNodes using 135 shots, however measurement statistics will be course grained across these 135 shots:
- All measurement statistics will first be computed using the first 5 shots --- that is, shots_range=[0, 5], bin_size=5.
- Next, the tuple (10, 3) indicates 10 shots, repeated 3 times. This will use shot_range=[5, 35], performing the expectation value in bins of size 10 (bin_size=10).
- Finally, we repeat the measurement statistics for the final 100 shots, shot_range=[35, 135], bin_size=100.
The old PennyLane core has been removed, including the following modules: (#1100)
- pennylane.variables
- pennylane.qnodes
As part of this change, the location of the new core within the Python module has been moved:
- Moves pennylane.tape.interfaces → pennylane.interfaces
- Merges pennylane.CircuitGraph and pennylane.TapeCircuitGraph → pennylane.CircuitGraph
- Merges pennylane.OperationRecorder and pennylane.TapeOperationRecorder →
- pennylane.tape.operation_recorder
- Merges pennylane.measure and pennylane.tape.measure → pennylane.measure
- Merges pennylane.operation and pennylane.tape.operation → pennylane.operation
- Merges pennylane._queuing and pennylane.tape.queuing → pennylane.queuing
This has no affect on import location.

In addition,
- All tape-mode functions have been removed (qml.enable_tape(), qml.tape_mode_active()),
- All tape fixtures have been deleted,
- Tests specifically for non-tape mode have been deleted.
The device test suite no longer accepts the analytic keyword. (#1216)

Bug fixes

Fixes a bug where using the circuit drawer with a ControlledQubitUnitary operation raised an error. (#1174)
Fixes a bug and a test where the QuantumTape.is_sampled attribute was not being updated. (#1126)
Fixes a bug where BasisEmbedding would not accept inputs whose bits are all ones or all zeros. (#1114)
The ExpvalCost class raises an error if instantiated with non-expectation measurement statistics. (#1106)
Fixes a bug where decompositions would reset the differentiation method of a QNode. (#1117)
Fixes a bug where the second-order CV parameter-shift rule would error if attempting to compute the gradient of a QNode with more than one second-order observable. (#1197)
Fixes a bug where repeated Torch interface applications after expansion caused an error. (#1223)
Sampling works correctly with batches of shots specified as a list. (#1232)

Documentation

Updated the diagram used in the Architectural overview page of the Development guide such that it doesn't mention Variables. (#1235)
Typos addressed in templates documentation. (#1094)
Upgraded the documentation to use Sphinx 3.5.3 and the new m2r2 package. (#1186)
Added flaky as dependency for running tests in the documentation. (#1113)

Contributors

This release contains contributions from (in alphabetical order):

Shahnawaz Ahmed, Juan Miguel Arrazola, Thomas Bromley, Olivia Di Matteo, Alain Delgado Gran, Kyle Godbey, Diego Guala, Theodor Isacsson, Josh Izaac, Soran Jahangiri, Nathan Killoran, Christina Lee, Daniel Polatajko, Chase Roberts, Sankalp Sanand, Pritish Sehzpaul, Maria Schuld, Antal Száva, David Wierichs.

Release 0.14.1

Bug fixes

Fixes a testing bug where tests that required JAX would fail if JAX was not installed. The tests will now instead be skipped if JAX can not be imported. (#1066)
Fixes a bug where inverse operations could not be differentiated using backpropagation on default.qubit. (#1072)
The QNode has a new keyword argument, max_expansion, that determines the maximum number of times the internal circuit should be expanded when executed on a device. In addition, the default number of max expansions has been increased from 2 to 10, allowing devices that require more than two operator decompositions to be supported. (#1074)
Fixes a bug where Hamiltonian objects created with non-list arguments raised an error for arithmetic operations. (#1082)
Fixes a bug where Hamiltonian objects with no coefficients or operations would return a faulty result when used with ExpvalCost. (#1082)

Documentation

Updates mentions of generate_hamiltonian to molecular_hamiltonian in the docstrings of the ExpvalCost and Hamiltonian classes. (#1077)

Contributors

This release contains contributions from (in alphabetical order):

Thomas Bromley, Josh Izaac, Antal Száva.

Release 0.14.0

New features since last release

Perform quantum machine learning with JAX

QNodes created with default.qubit now support a JAX interface, allowing JAX to be used to create, differentiate, and optimize hybrid quantum-classical models. (#947)

This is supported internally via a new default.qubit.jax device. This device runs end to end in JAX, meaning that it supports all of the awesome JAX transformations (jax.vmap, jax.jit, jax.hessian, etc).

Here is an example of how to use the new JAX interface:
```
dev = qml.device("default.qubit", wires=1)
@qml.qnode(dev, interface="jax", diff_method="backprop")
def circuit(x):
    qml.RX(x[1], wires=0)
    qml.Rot(x[0], x[1], x[2], wires=0)
    return qml.expval(qml.PauliZ(0))

weights = jnp.array([0.2, 0.5, 0.1])
grad_fn = jax.grad(circuit)
print(grad_fn(weights))
```
Currently, only diff_method="backprop" is supported, with plans to support more in the future.

New, faster, quantum gradient methods

A new differentiation method has been added for use with simulators. The "adjoint" method operates after a forward pass by iteratively applying inverse gates to scan backwards through the circuit. (#1032)

This method is similar to the reversible method, but has a lower time overhead and a similar memory overhead. It follows the approach provided by Jones and Gacon. This method is only compatible with certain statevector-based devices such as default.qubit.

Example use:
```
import pennylane as qml

wires = 1
device = qml.device("default.qubit", wires=wires)

@qml.qnode(device, diff_method="adjoint")
def f(params):
    qml.RX(0.1, wires=0)
    qml.Rot(*params, wires=0)
    qml.RX(-0.3, wires=0)
    return qml.expval(qml.PauliZ(0))

params = [0.1, 0.2, 0.3]
qml.grad(f)(params)
```
The default logic for choosing the 'best' differentiation method has been altered to improve performance. (#1008)
- If the quantum device provides its own gradient, this is now the preferred differentiation method.
- If the quantum device natively supports classical backpropagation, this is now preferred over the parameter-shift rule.
  
  This will lead to marked speed improvement during optimization when using default.qubit, with a sight penalty on the forward-pass evaluation.
More details are available below in the 'Improvements' section for plugin developers.
PennyLane now supports analytical quantum gradients for noisy channels, in addition to its existing support for unitary operations. The noisy channels BitFlip, PhaseFlip, and DepolarizingChannel all support analytic gradients out of the box. (#968)

A method has been added for calculating the Hessian of quantum circuits using the second-order parameter shift formula. (#961)

The following example shows the calculation of the Hessian:

n_wires = 5
weights = [2.73943676, 0.16289932, 3.4536312, 2.73521126, 2.6412488]

dev = qml.device("default.qubit", wires=n_wires)

with qml.tape.QubitParamShiftTape() as tape:
    for i in range(n_wires):
        qml.RX(weights[i], wires=i)

    qml.CNOT(wires=[0, 1])
    qml.CNOT(wires=[2, 1])
    qml.CNOT(wires=[3, 1])
    qml.CNOT(wires=[4, 3])

    qml.expval(qml.PauliZ(1))

print(tape.hessian(dev))

The Hessian is not yet supported via classical machine learning interfaces, but will be added in a future release.

More operations and templates

Two new error channels, BitFlip and PhaseFlip have been added. (#954)

They can be used in the same manner as existing error channels:

dev = qml.device("default.mixed", wires=2)

@qml.qnode(dev)
def circuit():
    qml.RX(0.3, wires=0)
    qml.RY(0.5, wires=1)
    qml.BitFlip(0.01, wires=0)
    qml.PhaseFlip(0.01, wires=1)
    return qml.expval(qml.PauliZ(0))

Apply permutations to wires using the Permute subroutine. (#952)

import pennylane as qml
dev = qml.device('default.qubit', wires=5)

@qml.qnode(dev)
def apply_perm():
    # Send contents of wire 4 to wire 0, of wire 2 to wire 1, etc.
    qml.templates.Permute([4, 2, 0, 1, 3], wires=dev.wires)
    return qml.expval(qml.PauliZ(0))

QNode transformations

The qml.metric_tensor function transforms a QNode to produce the Fubini-Study metric tensor with full autodifferentiation support---even on hardware. (#1014)

Consider the following QNode:

dev = qml.device("default.qubit", wires=3)

@qml.qnode(dev, interface="autograd")
def circuit(weights):
    # layer 1
    qml.RX(weights[0, 0], wires=0)
    qml.RX(weights[0, 1], wires=1)

    qml.CNOT(wires=[0, 1])
    qml.CNOT(wires=[1, 2])

    # layer 2
    qml.RZ(weights[1, 0], wires=0)
    qml.RZ(weights[1, 1], wires=2)

    qml.CNOT(wires=[0, 1])
    qml.CNOT(wires=[1, 2])
    return qml.expval(qml.PauliZ(0) @ qml.PauliZ(1)), qml.expval(qml.PauliY(2))

We can use the metric_tensor function to generate a new function, that returns the metric tensor of this QNode:

>>> met_fn = qml.metric_tensor(circuit)
>>> weights = np.array([[0.1, 0.2, 0.3], [0.4, 0.5, 0.6]], requires_grad=True)
>>> met_fn(weights)
tensor([[0.25  , 0.    , 0.    , 0.    ],
        [0.    , 0.25  , 0.    , 0.    ],
        [0.    , 0.    , 0.0025, 0.0024],
        [0.    , 0.    , 0.0024, 0.0123]], requires_grad=True)

The returned metric tensor is also fully differentiable, in all interfaces. For example, differentiating the (3, 2) element:

>>> grad_fn = qml.grad(lambda x: met_fn(x)[3, 2])
>>> grad_fn(weights)
array([[ 0.04867729, -0.00049502,  0.        ],
       [ 0.        ,  0.        ,  0.        ]])

Differentiation is also supported using Torch, Jax, and TensorFlow.

Adds the new function qml.math.cov_matrix(). This function accepts a list of commuting observables, and the probability distribution in the shared observable eigenbasis after the application of an ansatz. It uses these to construct the covariance matrix in a framework independent manner, such that the output covariance matrix is autodifferentiable. (#1012)

For example, consider the following ansatz and observable list:

obs_list = [qml.PauliX(0) @ qml.PauliZ(1), qml.PauliY(2)]
ansatz = qml.templates.StronglyEntanglingLayers

We can construct a QNode to output the probability distribution in the shared eigenbasis of the observables:

dev = qml.device("default.qubit", wires=3)

@qml.qnode(dev, interface="autograd")
def circuit(weights):
    ansatz(weights, wires=[0, 1, 2])
    # rotate into the basis of the observables
    for o in obs_list:
        o.diagonalizing_gates()
    return qml.probs(wires=[0, 1, 2])

We can now compute the covariance matrix:

>>> weights = qml.init.strong_ent_layers_normal(n_layers=2, n_wires=3)
>>> cov = qml.math.cov_matrix(circuit(weights), obs_list)
>>> cov
array([[0.98707611, 0.03665537],
       [0.03665537, 0.99998377]])

Autodifferentiation is fully supported using all interfaces:

>>> cost_fn = lambda weights: qml.math.cov_matrix(circuit(weights), obs_list)[0, 1]
>>> qml.grad(cost_fn)(weights)[0]
array([[[ 4.94240914e-17, -2.33786398e-01, -1.54193959e-01],
        [-3.05414996e-17,  8.40072236e-04,  5.57884080e-04],
        [ 3.01859411e-17,  8.60411436e-03,  6.15745204e-04]],

       [[ 6.80309533e-04, -1.23162742e-03,  1.08729813e-03],
        [-1.53863193e-01, -1.38700657e-02, -1.36243323e-01],
        [-1.54665054e-01, -1.89018172e-02, -1.56415558e-01]]])

A new qml.draw function is available, allowing QNodes to be easily drawn without execution by providing example input. (#962)

@qml.qnode(dev)
def circuit(a, w):
    qml.Hadamard(0)
    qml.CRX(a, wires=[0, 1])
    qml.Rot(*w, wires=[1])
    qml.CRX(-a, wires=[0, 1])
    return qml.expval(qml.PauliZ(0) @ qml.PauliZ(1))

The QNode circuit structure may depend on the input arguments; this is taken into account by passing example QNode arguments to the qml.draw() drawing function:

>>> drawer = qml.draw(circuit)
>>> result = drawer(a=2.3, w=[1.2, 3.2, 0.7])
>>> print(result)
0: ──H──╭C────────────────────────────╭C─────────╭┤ ⟨Z ⊗ Z⟩
1: ─────╰RX(2.3)──Rot(1.2, 3.2, 0.7)──╰RX(-2.3)──╰┤ ⟨Z ⊗ Z⟩

A faster, leaner, and more flexible core

The new core of PennyLane, rewritten from the ground up and developed over the last few release cycles, has achieved feature parity and has been made the new default in PennyLane v0.14. The old core has been marked as deprecated, and will be removed in an upcoming release. (#1046) (#1040) (#1034) (#1035) (#1027) (#1026) (#1021) (#1054) (#1049)

While high-level PennyLane code and tutorials remain unchanged, the new core provides several advantages and improvements:
- Faster and more optimized: The new core provides various performance optimizations, reducing pre- and post-processing overhead, and reduces the number of quantum evaluations in certain cases.
- Support for in-QNode classical processing: this allows for differentiable classical processing within the QNode.
```
dev = qml.device("default.qubit", wires=1)

@qml.qnode(dev, interface="tf")
def circuit(p):
    qml.RX(tf.sin(p[0])**2 + p[1], wires=0)
    return qml.expval(qml.PauliZ(0))
```
  The classical processing functions used within the QNode must match the QNode interface. Here, we use TensorFlow:
```
>>> params = tf.Variable([0.5, 0.1], dtype=tf.float64)
>>> with tf.GradientTape() as tape:
...     res = circuit(params)
>>> grad = tape.gradient(res, params)
>>> print(res)
tf.Tensor(0.9460913127754935, shape=(), dtype=float64)
>>> print(grad)
tf.Tensor([-0.27255248 -0.32390003], shape=(2,), dtype=float64)
```
  As a result of this change, quantum decompositions that require classical processing are fully supported and end-to-end differentiable in tape mode.
- No more Variable wrapping: QNode arguments no longer become Variable objects within the QNode.
```
dev = qml.device("default.qubit", wires=1)

@qml.qnode(dev)
def circuit(x):
    print("Parameter value:", x)
    qml.RX(x, wires=0)
    return qml.expval(qml.PauliZ(0))
```
  Internal QNode parameters can be easily inspected, printed, and manipulated:
```
>>> circuit(0.5)
Parameter value: 0.5
tensor(0.87758256, requires_grad=True)
```
- Less restrictive QNode signatures: There is no longer any restriction on the QNode signature; the QNode can be defined and called following the same rules as standard Python functions.
  
  For example, the following QNode uses positional, named, and variable keyword arguments:
```
x = torch.tensor(0.1, requires_grad=True)
y = torch.tensor([0.2, 0.3], requires_grad=True)
z = torch.tensor(0.4, requires_grad=True)

@qml.qnode(dev, interface="torch")
def circuit(p1, p2=y, **kwargs):
    qml.RX(p1, wires=0)
    qml.RY(p2[0] * p2[1], wires=0)
    qml.RX(kwargs["p3"], wires=0)
    return qml.var(qml.PauliZ(0))
```
  When we call the QNode, we may pass the arguments by name even if defined positionally; any argument not provided will use the default value.
```
>>> res = circuit(p1=x, p3=z)
>>> print(res)
tensor(0.2327, dtype=torch.float64, grad_fn=<SelectBackward>)
>>> res.backward()
>>> print(x.grad, y.grad, z.grad)
tensor(0.8396) tensor([0.0289, 0.0193]) tensor(0.8387)
```
  This extends to the qnn module, where KerasLayer and TorchLayer modules can be created from QNodes with unrestricted signatures.
- Smarter measurements: QNodes can now measure wires more than once, as long as all observables are commuting:
```
@qml.qnode(dev)
def circuit(x):
    qml.RX(x, wires=0)
    return [
        qml.expval(qml.PauliZ(0)),
        qml.expval(qml.PauliZ(0) @ qml.PauliZ(1))
    ]
```
  Further, the qml.ExpvalCost() function allows for optimizing measurements to reduce the number of quantum evaluations required.
With the new PennyLane core, there are a few small breaking changes, detailed below in the 'Breaking Changes' section.

Improvements

The built-in PennyLane optimizers allow more flexible cost functions. The cost function passed to most optimizers may accept any combination of trainable arguments, non-trainable arguments, and keyword arguments. (#959) (#1053)

The full changes apply to:

AdagradOptimizer
AdamOptimizer
GradientDescentOptimizer
MomentumOptimizer
NesterovMomentumOptimizer
RMSPropOptimizer
RotosolveOptimizer

The requires_grad=False property must mark any non-trainable constant argument. The RotoselectOptimizer allows passing only keyword arguments.

Example use:

def cost(x, y, data, scale=1.0):
    return scale * (x[0]-data)**2 + scale * (y-data)**2

x = np.array([1.], requires_grad=True)
y = np.array([1.0])
data = np.array([2.], requires_grad=False)

opt = qml.GradientDescentOptimizer()

# the optimizer step and step_and_cost methods can
# now update multiple parameters at once
x_new, y_new, data = opt.step(cost, x, y, data, scale=0.5)
(x_new, y_new, data), value = opt.step_and_cost(cost, x, y, data, scale=0.5)

# list and tuple unpacking is also supported
params = (x, y, data)
params = opt.step(cost, *params)

The circuit drawer has been updated to support the inclusion of unused or inactive wires, by passing the show_all_wires argument. (#1033)

dev = qml.device('default.qubit', wires=[-1, "a", "q2", 0])

@qml.qnode(dev)
def circuit():
    qml.Hadamard(wires=-1)
    qml.CNOT(wires=[-1, "q2"])
    return qml.expval(qml.PauliX(wires="q2"))

>>> print(qml.draw(circuit, show_all_wires=True)())
>>>
 -1: ──H──╭C──┤
  a: ─────│───┤
 q2: ─────╰X──┤ ⟨X⟩
  0: ─────────┤

The logic for choosing the 'best' differentiation method has been altered to improve performance. (#1008)
- If the device provides its own gradient, this is now the preferred differentiation method.
- If a device provides additional interface-specific versions that natively support classical backpropagation, this is now preferred over the parameter-shift rule.
  
  Devices define additional interface-specific devices via their capabilities() dictionary. For example, default.qubit supports supplementary devices for TensorFlow, Autograd, and JAX:
```
{
  "passthru_devices": {
      "tf": "default.qubit.tf",
      "autograd": "default.qubit.autograd",
      "jax": "default.qubit.jax",
  },
}
```
As a result of this change, if the QNode diff_method is not explicitly provided, it is possible that the QNode will run on a supplementary device of the device that was specifically provided:
```
dev = qml.device("default.qubit", wires=2)
qml.QNode(dev) # will default to backprop on default.qubit.autograd
qml.QNode(dev, interface="tf") # will default to backprop on default.qubit.tf
qml.QNode(dev, interface="jax") # will default to backprop on default.qubit.jax
```
The default.qubit device has been updated so that internally it applies operations in a more functional style, i.e., by accepting an input state and returning an evolved state. (#1025)
A new test series, pennylane/devices/tests/test_compare_default_qubit.py, has been added, allowing to test if a chosen device gives the same result as default.qubit. (#897)

Three tests are added:
- test_hermitian_expectation,
- test_pauliz_expectation_analytic, and
- test_random_circuit.
Adds the following agnostic tensor manipulation functions to the qml.math module: abs, angle, arcsin, concatenate, dot, squeeze, sqrt, sum, take, where. These functions are required to fully support end-to-end differentiable Mottonen and Amplitude embedding. (#922) (#1011)
The qml.math module now supports JAX. (#985)
Several improvements have been made to the Wires class to reduce overhead and simplify the logic of how wire labels are interpreted: (#1019) (#1010) (#1005) (#983) (#967)
- If the input wires to a wires class instantiation Wires(wires) can be iterated over, its elements are interpreted as wire labels. Otherwise, wires is interpreted as a single wire label. The only exception to this are strings, which are always interpreted as a single wire label, so users can address wires with labels such as "ancilla".
- Any type can now be a wire label as long as it is hashable. The hash is used to establish the uniqueness of two labels.
- Indexing wires objects now returns a label, instead of a new Wires object. For example:
```
>>> w = Wires([0, 1, 2])
>>> w[1]
>>> 1
```
- The check for uniqueness of wires moved from Wires instantiation to the qml.wires._process function in order to reduce overhead from repeated creation of Wires instances.
- Calls to the Wires class are substantially reduced, for example by avoiding to call Wires on Wires instances on Operation instantiation, and by using labels instead of Wires objects inside the default qubit device.
Adds the PauliRot generator to the qml.operation module. This generator is required to construct the metric tensor. (#963)
The templates are modified to make use of the new qml.math module, for framework-agnostic tensor manipulation. This allows the template library to be differentiable in backpropagation mode (diff_method="backprop"). (#873)

The circuit drawer now allows for the wire order to be (optionally) modified: (#992)

>>> dev = qml.device('default.qubit', wires=["a", -1, "q2"])
>>> @qml.qnode(dev)
... def circuit():
...     qml.Hadamard(wires=-1)
...     qml.CNOT(wires=["a", "q2"])
...     qml.RX(0.2, wires="a")
...     return qml.expval(qml.PauliX(wires="q2"))

Printing with default wire order of the device:

>>> print(circuit.draw())
  a: ─────╭C──RX(0.2)──┤
 -1: ──H──│────────────┤
 q2: ─────╰X───────────┤ ⟨X⟩

Changing the wire order:

>>> print(circuit.draw(wire_order=["q2", "a", -1]))
 q2: ──╭X───────────┤ ⟨X⟩
  a: ──╰C──RX(0.2)──┤
 -1: ───H───────────┤

Breaking changes

QNodes using the new PennyLane core will no longer accept ragged arrays as inputs.

When using the new PennyLane core and the Autograd interface, non-differentiable data passed as a QNode argument or a gate must have the requires_grad property set to False:

@qml.qnode(dev)
def circuit(weights, data):
    basis_state = np.array([1, 0, 1, 1], requires_grad=False)
    qml.BasisState(basis_state, wires=[0, 1, 2, 3])
    qml.templates.AmplitudeEmbedding(data, wires=[0, 1, 2, 3])
    qml.templates.BasicEntanglerLayers(weights, wires=[0, 1, 2, 3])
    return qml.probs(wires=0)

data = np.array(data, requires_grad=False)
weights = np.array(weights, requires_grad=True)
circuit(weights, data)

Bug fixes

Fixes an issue where if the constituent observables of a tensor product do not exist in the queue, an error is raised. With this fix, they are first queued before annotation occurs. (#1038)
Fixes an issue with tape expansions where information about sampling (specifically the is_sampled tape attribute) was not preserved. (#1027)
Tape expansion was not properly taking into devices that supported inverse operations, causing inverse operations to be unnecessarily decomposed. The QNode tape expansion logic, as well as the Operation.expand() method, has been modified to fix this. (#956)
Fixes an issue where the Autograd interface was not unwrapping non-differentiable PennyLane tensors, which can cause issues on some devices. (#941)
qml.vqe.Hamiltonian prints any observable with any number of strings. (#987)
Fixes a bug where parameter-shift differentiation would fail if the QNode contained a single probability output. (#1007)
Fixes an issue when using trainable parameters that are lists/arrays with tape.vjp. (#1042)
The TensorN observable is updated to support being copied without any parameters or wires passed. (#1047)
Fixed deprecation warning when importing Sequence from collections instead of collections.abc in vqe/vqe.py. (#1051)

Contributors

This release contains contributions from (in alphabetical order):

Juan Miguel Arrazola, Thomas Bromley, Olivia Di Matteo, Theodor Isacsson, Josh Izaac, Christina Lee, Alejandro Montanez, Steven Oud, Chase Roberts, Sankalp Sanand, Maria Schuld, Antal Száva, David Wierichs, Jiahao Yao.

Release 0.13.0

New features since last release

Automatically optimize the number of measurements

QNodes in tape mode now support returning observables on the same wire whenever the observables are qubit-wise commuting Pauli words. Qubit-wise commuting observables can be evaluated with a single device run as they are diagonal in the same basis, via a shared set of single-qubit rotations. (#882)

The following example shows a single QNode returning the expectation values of the qubit-wise commuting Pauli words XX and XI:
```
qml.enable_tape()

@qml.qnode(dev)
def f(x):
    qml.Hadamard(wires=0)
    qml.Hadamard(wires=1)
    qml.CRot(0.1, 0.2, 0.3, wires=[1, 0])
    qml.RZ(x, wires=1)
    return qml.expval(qml.PauliX(0) @ qml.PauliX(1)), qml.expval(qml.PauliX(0))
```
```
>>> f(0.4)
tensor([0.89431013, 0.9510565 ], requires_grad=True)
```

The ExpvalCost class (previously VQECost) now provides observable optimization using the optimize argument, resulting in potentially fewer device executions. (#902)

This is achieved by separating the observables composing the Hamiltonian into qubit-wise commuting groups and evaluating those groups on a single QNode using functionality from the qml.grouping module:

qml.enable_tape()
commuting_obs = [qml.PauliX(0), qml.PauliX(0) @ qml.PauliZ(1)]
H = qml.vqe.Hamiltonian([1, 1], commuting_obs)

dev = qml.device("default.qubit", wires=2)
ansatz = qml.templates.StronglyEntanglingLayers

cost_opt = qml.ExpvalCost(ansatz, H, dev, optimize=True)
cost_no_opt = qml.ExpvalCost(ansatz, H, dev, optimize=False)

params = qml.init.strong_ent_layers_uniform(3, 2)

Grouping these commuting observables leads to fewer device executions:

>>> cost_opt(params)
>>> ex_opt = dev.num_executions
>>> cost_no_opt(params)
>>> ex_no_opt = dev.num_executions - ex_opt
>>> print("Number of executions:", ex_no_opt)
Number of executions: 2
>>> print("Number of executions (optimized):", ex_opt)
Number of executions (optimized): 1

New quantum gradient features

Compute the analytic gradient of quantum circuits in parallel on supported devices. (#840)

This release introduces support for batch execution of circuits, via a new device API method Device.batch_execute(). Devices that implement this new API support submitting a batch of circuits for parallel evaluation simultaneously, which can significantly reduce the computation time.

Furthermore, if using tape mode and a compatible device, gradient computations will automatically make use of the new batch API---providing a speedup during optimization.
Gradient recipes are now much more powerful, allowing for operations to define their gradient via an arbitrary linear combination of circuit evaluations. (#909) (#915)

With this change, gradient recipes can now be of the form :math:\frac{\partial}{\partial\phi_k}f(\phi_k) = \sum_{i} c_i f(a_i \phi_k + s_i ), and are no longer restricted to two-term shifts with identical (but opposite in sign) shift values.

As a result, PennyLane now supports native analytic quantum gradients for the controlled rotation operations CRX, CRY, CRZ, and CRot. This allows for parameter-shift analytic gradients on hardware, without decomposition.

Note that this is a breaking change for developers; please see the Breaking Changes section for more details.

The qnn.KerasLayer class now supports differentiating the QNode through classical backpropagation in tape mode. (#869)

qml.enable_tape()

dev = qml.device("default.qubit.tf", wires=2)

@qml.qnode(dev, interface="tf", diff_method="backprop")
def f(inputs, weights):
    qml.templates.AngleEmbedding(inputs, wires=range(2))
    qml.templates.StronglyEntanglingLayers(weights, wires=range(2))
    return [qml.expval(qml.PauliZ(i)) for i in range(2)]

weight_shapes = {"weights": (3, 2, 3)}

qlayer = qml.qnn.KerasLayer(f, weight_shapes, output_dim=2)

inputs = tf.constant(np.random.random((4, 2)), dtype=tf.float32)

with tf.GradientTape() as tape:
    out = qlayer(inputs)

tape.jacobian(out, qlayer.trainable_weights)

New operations, templates, and measurements

Adds the qml.density_matrix QNode return with partial trace capabilities. (#878)

The density matrix over the provided wires is returned, with all other subsystems traced out. qml.density_matrix currently works for both the default.qubit and default.mixed devices.
```
qml.enable_tape()
dev = qml.device("default.qubit", wires=2)

def circuit(x):
    qml.PauliY(wires=0)
    qml.Hadamard(wires=1)
    return qml.density_matrix(wires=[1])  # wire 0 is traced out
```

Adds the square-root X gate SX. (#871)

dev = qml.device("default.qubit", wires=1)

@qml.qnode(dev)
def circuit():
    qml.SX(wires=[0])
    return qml.expval(qml.PauliZ(wires=[0]))

Two new hardware-efficient particle-conserving templates have been implemented to perform VQE-based quantum chemistry simulations. The new templates apply several layers of the particle-conserving entanglers proposed in Figs. 2a and 2b of Barkoutsos et al., arXiv:1805.04340 (#875) (#876)

Estimate and track resources

The QuantumTape class now contains basic resource estimation functionality. The method tape.get_resources() returns a dictionary with a list of the constituent operations and the number of times they appear in the circuit. Similarly, tape.get_depth() computes the circuit depth. (#862)

>>> with qml.tape.QuantumTape() as tape:
...    qml.Hadamard(wires=0)
...    qml.RZ(0.26, wires=1)
...    qml.CNOT(wires=[1, 0])
...    qml.Rot(1.8, -2.7, 0.2, wires=0)
...    qml.Hadamard(wires=1)
...    qml.CNOT(wires=[0, 1])
...    qml.expval(qml.PauliZ(0) @ qml.PauliZ(1))
>>> tape.get_resources()
{'Hadamard': 2, 'RZ': 1, 'CNOT': 2, 'Rot': 1}
>>> tape.get_depth()
4

The number of device executions over a QNode's lifetime can now be returned using num_executions. (#853)

>>> dev = qml.device("default.qubit", wires=2)
>>> @qml.qnode(dev)
... def circuit(x, y):
...    qml.RX(x, wires=[0])
...    qml.RY(y, wires=[1])
...    qml.CNOT(wires=[0, 1])
...    return qml.expval(qml.PauliZ(0) @ qml.PauliX(1))
>>> for _ in range(10):
...    circuit(0.432, 0.12)
>>> print(dev.num_executions)
10

Improvements

Support for tape mode has improved across PennyLane. The following features now work in tape mode:
- QNode collections (#863)
- qnn.ExpvalCost (#863) (#911)
- qml.qnn.KerasLayer (#869)
- qml.qnn.TorchLayer (#865)
- The qml.qaoa module (#905)
A new function, qml.refresh_devices(), has been added, allowing PennyLane to rescan installed PennyLane plugins and refresh the device list. In addition, the qml.device loader will attempt to refresh devices if the required plugin device cannot be found. This will result in an improved experience if installing PennyLane and plugins within a running Python session (for example, on Google Colab), and avoid the need to restart the kernel/runtime. (#907)

When using grad_fn = qml.grad(cost) to compute the gradient of a cost function with the Autograd interface, the value of the intermediate forward pass is now available via the grad_fn.forward property (#914):

def cost_fn(x, y):
    return 2 * np.sin(x[0]) * np.exp(-x[1]) + x[0] ** 3 + np.cos(y)

params = np.array([0.1, 0.5], requires_grad=True)
data = np.array(0.65, requires_grad=False)
grad_fn = qml.grad(cost_fn)

grad_fn(params, data)  # perform backprop and evaluate the gradient
grad_fn.forward  # the cost function value

Gradient-based optimizers now have a step_and_cost method that returns both the next step as well as the objective (cost) function output. (#916)
```
>>> opt = qml.GradientDescentOptimizer()
>>> params, cost = opt.step_and_cost(cost_fn, params)
```
PennyLane provides a new experimental module qml.proc which provides framework-agnostic processing functions for array and tensor manipulations. (#886)

Given the input tensor-like object, the call is dispatched to the corresponding array manipulation framework, allowing for end-to-end differentiation to be preserved.
```
>>> x = torch.tensor([1., 2.])
>>> qml.proc.ones_like(x)
tensor([1, 1])
>>> y = tf.Variable([[0], [5]])
>>> qml.proc.ones_like(y, dtype=np.complex128)
<tf.Tensor: shape=(2, 1), dtype=complex128, numpy=
array([[1.+0.j],
       [1.+0.j]])>
```
Note that these functions are experimental, and only a subset of common functionality is supported. Furthermore, the names and behaviour of these functions may differ from similar functions in common frameworks; please refer to the function docstrings for more details.
The gradient methods in tape mode now fully separate the quantum and classical processing. Rather than returning the evaluated gradients directly, they now return a tuple containing the required quantum and classical processing steps. (#840)
```
def gradient_method(idx, param, **options):
    # generate the quantum tapes that must be computed
    # to determine the quantum gradient
    tapes = quantum_gradient_tapes(self)

    def processing_fn(results):
        # perform classical processing on the evaluated tapes
        # returning the evaluated quantum gradient
        return classical_processing(results)

    return tapes, processing_fn
```
The JacobianTape.jacobian() method has been similarly modified to accumulate all gradient quantum tapes and classical processing functions, evaluate all quantum tapes simultaneously, and then apply the post-processing functions to the evaluated tape results.
The MultiRZ gate now has a defined generator, allowing it to be used in quantum natural gradient optimization. (#912)
The CRot gate now has a decomposition method, which breaks the gate down into rotations and CNOT gates. This allows CRot to be used on devices that do not natively support it. (#908)
The classical processing in the MottonenStatePreparation template has been largely rewritten to use dense matrices and tensor manipulations wherever possible. This is in preparation to support differentiation through the template in the future. (#864)
Device-based caching has replaced QNode caching. Caching is now accessed by passing a cache argument to the device. (#851)

The cache argument should be an integer specifying the size of the cache. For example, a cache of size 10 is created using:
```
>>> dev = qml.device("default.qubit", wires=2, cache=10)
```
The Operation, Tensor, and MeasurementProcess classes now have the __copy__ special method defined. (#840)

This allows us to ensure that, when a shallow copy is performed of an operation, the mutable list storing the operation parameters is also shallow copied. Both the old operation and the copied operation will continue to share the same parameter data,
```
>>> import copy
>>> op = qml.RX(0.2, wires=0)
>>> op2 = copy.copy(op)
>>> op.data[0] is op2.data[0]
True
```
however the list container is not a reference:
```
>>> op.data is op2.data
False
```
This allows the parameters of the copied operation to be modified, without mutating the parameters of the original operation.
The QuantumTape.copy method has been tweaked so that (#840):
- Optionally, the tape's operations are shallow copied in addition to the tape by passing the copy_operations=True boolean flag. This allows the copied tape's parameters to be mutated without affecting the original tape's parameters. (Note: the two tapes will share parameter data until one of the tapes has their parameter list modified.)
- Copied tapes can be cast to another QuantumTape subclass by passing the tape_cls keyword argument.

Breaking changes

Updated how parameter-shift gradient recipes are defined for operations, allowing for gradient recipes that are specified as an arbitrary number of terms. (#909)

Previously, Operation.grad_recipe was restricted to two-term parameter-shift formulas. With this change, the gradient recipe now contains elements of the form :math:[c_i, a_i, s_i], resulting in a gradient recipe of :math:\frac{\partial}{\partial\phi_k}f(\phi_k) = \sum_{i} c_i f(a_i \phi_k + s_i ).

As this is a breaking change, all custom operations with defined gradient recipes must be updated to continue working with PennyLane 0.13. Note though that if grad_recipe = None, the default gradient recipe remains unchanged, and corresponds to the two terms :math:[c_0, a_0, s_0]=[1/2, 1, \pi/2] and :math:[c_1, a_1, s_1]=[-1/2, 1, -\pi/2] for every parameter.

The VQECost class has been renamed to ExpvalCost to reflect its general applicability beyond VQE. Use of VQECost is still possible but will result in a deprecation warning. (#913)

Bug fixes

The default.qubit.tf device is updated to handle TensorFlow objects (e.g., tf.Variable) as gate parameters correctly when using the MultiRZ and CRot operations. (#921)
PennyLane tensor objects are now unwrapped in BaseQNode when passed as a keyword argument to the quantum function. (#903) (#893)
The new tape mode now prevents multiple observables from being evaluated on the same wire if the observables are not qubit-wise commuting Pauli words. (#882)
Fixes a bug in default.qubit whereby inverses of common gates were not being applied via efficient gate-specific methods, instead falling back to matrix-vector multiplication. The following gates were affected: PauliX, PauliY, PauliZ, Hadamard, SWAP, S, T, CNOT, CZ. (#872)
The PauliRot operation now gracefully handles single-qubit Paulis, and all-identity Paulis (#860).
Fixes a bug whereby binary Python operators were not properly propagating the requires_grad attribute to the output tensor. (#889)
Fixes a bug which prevents TorchLayer from doing backward when CUDA is enabled. (#899)
Fixes a bug where multi-threaded execution of QNodeCollection sometimes fails because of simultaneous queuing. This is fixed by adding thread locking during queuing. (#910)
Fixes a bug in QuantumTape.set_parameters(). The previous implementation assumed that the self.trainable_parms set would always be iterated over in increasing integer order. However, this is not guaranteed behaviour, and can lead to the incorrect tape parameters being set if this is not the case. (#923)
Fixes broken error message if a QNode is instantiated with an unknown exception. (#930)

Contributors

This release contains contributions from (in alphabetical order):

Juan Miguel Arrazola, Thomas Bromley, Christina Lee, Alain Delgado Gran, Olivia Di Matteo, Anthony Hayes, Theodor Isacsson, Josh Izaac, Soran Jahangiri, Nathan Killoran, Shumpei Kobayashi, Romain Moyard, Zeyue Niu, Maria Schuld, Antal Száva.

Release 0.12.0

New features since last release

New and improved simulators

PennyLane now supports a new device, default.mixed, designed for simulating mixed-state quantum computations. This enables native support for implementing noisy channels in a circuit, which generally map pure states to mixed states. (#794) (#807) (#819)

The device can be initialized as
```
>>> dev = qml.device("default.mixed", wires=1)
```
This allows the construction of QNodes that include non-unitary operations, such as noisy channels:
```
>>> @qml.qnode(dev)
... def circuit(params):
...     qml.RX(params[0], wires=0)
...     qml.RY(params[1], wires=0)
...     qml.AmplitudeDamping(0.5, wires=0)
...     return qml.expval(qml.PauliZ(0))
>>> print(circuit([0.54, 0.12]))
0.9257702929524184
>>> print(circuit([0, np.pi]))
0.0
```

New tools for optimizing measurements

The new grouping module provides functionality for grouping simultaneously measurable Pauli word observables. (#761) (#850) (#852)
- The optimize_measurements function will take as input a list of Pauli word observables and their corresponding coefficients (if any), and will return the partitioned Pauli terms diagonalized in the measurement basis and the corresponding diagonalizing circuits.
```
from pennylane.grouping import optimize_measurements
h, nr_qubits = qml.qchem.molecular_hamiltonian("h2", "h2.xyz")
rotations, grouped_ops, grouped_coeffs = optimize_measurements(h.ops, h.coeffs, grouping="qwc")
```
  The diagonalizing circuits of rotations correspond to the diagonalized Pauli word groupings of grouped_ops.
- Pauli word partitioning utilities are performed by the PauliGroupingStrategy class. An input list of Pauli words can be partitioned into mutually commuting, qubit-wise-commuting, or anticommuting groupings.
  
  For example, partitioning Pauli words into anticommutative groupings by the Recursive Largest First (RLF) graph colouring heuristic:
```
from pennylane import PauliX, PauliY, PauliZ, Identity
from pennylane.grouping import group_observables
pauli_words = [
    Identity('a') @ Identity('b'),
    Identity('a') @ PauliX('b'),
    Identity('a') @ PauliY('b'),
    PauliZ('a') @ PauliX('b'),
    PauliZ('a') @ PauliY('b'),
    PauliZ('a') @ PauliZ('b')
]
groupings = group_observables(pauli_words, grouping_type='anticommuting', method='rlf')
```
- Various utility functions are included for obtaining and manipulating Pauli words in the binary symplectic vector space representation.
  
  For instance, two Pauli words may be converted to their binary vector representation:
```
>>> from pennylane.grouping import pauli_to_binary
>>> from pennylane.wires import Wires
>>> wire_map = {Wires('a'): 0, Wires('b'): 1}
>>> pauli_vec_1 = pauli_to_binary(qml.PauliX('a') @ qml.PauliY('b'))
>>> pauli_vec_2 = pauli_to_binary(qml.PauliZ('a') @ qml.PauliZ('b'))
>>> pauli_vec_1
[1. 1. 0. 1.]
>>> pauli_vec_2
[0. 0. 1. 1.]
```
  Their product up to a phase may be computed by taking the sum of their binary vector representations, and returned in the operator representation.
```
>>> from pennylane.grouping import binary_to_pauli
>>> binary_to_pauli((pauli_vec_1 + pauli_vec_2) % 2, wire_map)
Tensor product ['PauliY', 'PauliX']: 0 params, wires ['a', 'b']
```
  For more details on the grouping module, see the grouping module documentation

Returning the quantum state from simulators

The quantum state of a QNode can now be returned using the qml.state() return function. (#818)

import pennylane as qml

dev = qml.device("default.qubit", wires=3)
qml.enable_tape()

@qml.qnode(dev)
def qfunc(x, y):
    qml.RZ(x, wires=0)
    qml.CNOT(wires=[0, 1])
    qml.RY(y, wires=1)
    qml.CNOT(wires=[0, 2])
    return qml.state()

>>> qfunc(0.56, 0.1)
array([0.95985437-0.27601028j, 0.        +0.j        ,
       0.04803275-0.01381203j, 0.        +0.j        ,
       0.        +0.j        , 0.        +0.j        ,
       0.        +0.j        , 0.        +0.j        ])

Differentiating the state is currently available when using the classical backpropagation differentiation method (diff_method="backprop") with a compatible device, and when using the new tape mode.

New operations and channels

PennyLane now includes standard channels such as the Amplitude-damping, Phase-damping, and Depolarizing channels, as well as the ability to make custom qubit channels. (#760) (#766) (#778)
The controlled-Y operation is now available via qml.CY. For devices that do not natively support the controlled-Y operation, it will be decomposed into qml.RY, qml.CNOT, and qml.S operations. (#806)

Preview the next-generation PennyLane QNode

The new PennyLane tape module provides a re-formulated QNode class, rewritten from the ground-up, that uses a new QuantumTape object to represent the QNode's quantum circuit. Tape mode provides several advantages over the standard PennyLane QNode. (#785) (#792) (#796) (#800) (#803) (#804) (#805) (#808) (#810) (#811) (#815) (#820) (#823) (#824) (#829)
- Support for in-QNode classical processing: Tape mode allows for differentiable classical processing within the QNode.
- No more Variable wrapping: In tape mode, QNode arguments no longer become Variable objects within the QNode.
- Less restrictive QNode signatures: There is no longer any restriction on the QNode signature; the QNode can be defined and called following the same rules as standard Python functions.
- Unifying all QNodes: The tape-mode QNode merges all QNodes (including the JacobianQNode and the PassthruQNode) into a single unified QNode, with identical behaviour regardless of the differentiation type.
- Optimizations: Tape mode provides various performance optimizations, reducing pre- and post-processing overhead, and reduces the number of quantum evaluations in certain cases.
Note that tape mode is experimental, and does not currently have feature-parity with the existing QNode. Feedback and bug reports are encouraged and will help improve the new tape mode.

Tape mode can be enabled globally via the qml.enable_tape function, without changing your PennyLane code:
```
qml.enable_tape()
dev = qml.device("default.qubit", wires=1)

@qml.qnode(dev, interface="tf")
def circuit(p):
    print("Parameter value:", p)
    qml.RX(tf.sin(p[0])**2 + p[1], wires=0)
    return qml.expval(qml.PauliZ(0))
```
For more details, please see the tape mode documentation.

Improvements

QNode caching has been introduced, allowing the QNode to keep track of the results of previous device executions and reuse those results in subsequent calls. Note that QNode caching is only supported in the new and experimental tape-mode. (#817)

Caching is available by passing a caching argument to the QNode:

dev = qml.device("default.qubit", wires=2)
qml.enable_tape()

@qml.qnode(dev, caching=10)  # cache up to 10 evaluations
def qfunc(x):
    qml.RX(x, wires=0)
    qml.RX(0.3, wires=1)
    qml.CNOT(wires=[0, 1])
    return qml.expval(qml.PauliZ(1))

qfunc(0.1)  # first evaluation executes on the device
qfunc(0.1)  # second evaluation accesses the cached result

Sped up the application of certain gates in default.qubit by using array/tensor manipulation tricks. The following gates are affected: PauliX, PauliY, PauliZ, Hadamard, SWAP, S, T, CNOT, CZ. (#772)
The computation of marginal probabilities has been made more efficient for devices with a large number of wires, achieving in some cases a 5x speedup. (#799)
Adds arithmetic operations (addition, tensor product, subtraction, and scalar multiplication) between Hamiltonian, Tensor, and Observable objects, and inline arithmetic operations between Hamiltonians and other observables. (#765)

Hamiltonians can now easily be defined as sums of observables:
```
>>> H = 3 * qml.PauliZ(0) - (qml.PauliX(0) @ qml.PauliX(1)) + qml.Hamiltonian([4], [qml.PauliZ(0)])
>>> print(H)
(7.0) [Z0] + (-1.0) [X0 X1]
```

Adds compare() method to Observable and Hamiltonian classes, which allows for comparison between observable quantities. (#765)

>>> H = qml.Hamiltonian([1], [qml.PauliZ(0)])
>>> obs = qml.PauliZ(0) @ qml.Identity(1)
>>> print(H.compare(obs))
True

>>> H = qml.Hamiltonian([2], [qml.PauliZ(0)])
>>> obs = qml.PauliZ(1) @ qml.Identity(0)
>>> print(H.compare(obs))
False

Adds simplify() method to the Hamiltonian class. (#765)

>>> H = qml.Hamiltonian([1, 2], [qml.PauliZ(0), qml.PauliZ(0) @ qml.Identity(1)])
>>> H.simplify()
>>> print(H)
(3.0) [Z0]

Added a new bit-flip mixer to the qml.qaoa module. (#774)
Summation of two Wires objects is now supported and will return a Wires object containing the set of all wires defined by the terms in the summation. (#812)

Breaking changes

The PennyLane NumPy module now returns scalar (zero-dimensional) arrays where Python scalars were previously returned. (#820) (#833)

For example, this affects array element indexing, and summation:
```
>>> x = np.array([1, 2, 3], requires_grad=False)
>>> x[0]
tensor(1, requires_grad=False)
>>> np.sum(x)
tensor(6, requires_grad=True)
```
This may require small updates to user code. A convenience method, np.tensor.unwrap(), has been added to help ease the transition. This converts PennyLane NumPy tensors to standard NumPy arrays and Python scalars:
```
>>> x = np.array(1.543, requires_grad=False)
>>> x.unwrap()
1.543
```
Note, however, that information regarding array differentiability will be lost.
The device capabilities dictionary has been redesigned, for clarity and robustness. In particular, the capabilities dictionary is now inherited from the parent class, various keys have more expressive names, and all keys are now defined in the base device class. For more details, please refer to the developer documentation. (#781)

Bug fixes

Changed to use lists for storing variable values inside BaseQNode allowing complex matrices to be passed to QubitUnitary. (#773)
Fixed a bug within default.qubit, resulting in greater efficiency when applying a state vector to all wires on the device. (#849)

Documentation

Equations have been added to the qml.sample and qml.probs docstrings to clarify the mathematical foundation of the performed measurements. (#843)

Contributors

This release contains contributions from (in alphabetical order):

Aroosa Ijaz, Juan Miguel Arrazola, Thomas Bromley, Jack Ceroni, Alain Delgado Gran, Josh Izaac, Soran Jahangiri, Nathan Killoran, Robert Lang, Cedric Lin, Olivia Di Matteo, Nicolás Quesada, Maria Schuld, Antal Száva.

Release 0.11.0

New features since last release

New and improved simulators

Added a new device, default.qubit.autograd, a pure-state qubit simulator written using Autograd. This device supports classical backpropagation (diff_method="backprop"); this can be faster than the parameter-shift rule for computing quantum gradients when the number of parameters to be optimized is large. (#721)

>>> dev = qml.device("default.qubit.autograd", wires=1)
>>> @qml.qnode(dev, diff_method="backprop")
... def circuit(x):
...     qml.RX(x[1], wires=0)
...     qml.Rot(x[0], x[1], x[2], wires=0)
...     return qml.expval(qml.PauliZ(0))
>>> weights = np.array([0.2, 0.5, 0.1])
>>> grad_fn = qml.grad(circuit)
>>> print(grad_fn(weights))
array([-2.25267173e-01, -1.00864546e+00,  6.93889390e-18])

See the device documentation for more details.

A new experimental C++ state-vector simulator device is now available, lightning.qubit. It uses the C++ Eigen library to perform fast linear algebra calculations for simulating quantum state-vector evolution.

lightning.qubit is currently in beta; it can be installed via pip:
```
$ pip install pennylane-lightning
```
Once installed, it can be used as a PennyLane device:
```
>>> dev = qml.device("lightning.qubit", wires=2)
```
For more details, please see the lightning qubit documentation.

New algorithms and templates

Added built-in QAOA functionality via the new qml.qaoa module. (#712) (#718) (#741) (#720)

This includes the following features:
- New qml.qaoa.x_mixer and qml.qaoa.xy_mixer functions for defining Pauli-X and XY mixer Hamiltonians.
- MaxCut: The qml.qaoa.maxcut function allows easy construction of the cost Hamiltonian and recommended mixer Hamiltonian for solving the MaxCut problem for a supplied graph.
- Layers: qml.qaoa.cost_layer and qml.qaoa.mixer_layer take cost and mixer Hamiltonians, respectively, and apply the corresponding QAOA cost and mixer layers to the quantum circuit
For example, using PennyLane to construct and solve a MaxCut problem with QAOA:
```
wires = range(3)
graph = Graph([(0, 1), (1, 2), (2, 0)])
cost_h, mixer_h = qaoa.maxcut(graph)

def qaoa_layer(gamma, alpha):
    qaoa.cost_layer(gamma, cost_h)
    qaoa.mixer_layer(alpha, mixer_h)

def antatz(params, **kwargs):

    for w in wires:
        qml.Hadamard(wires=w)

    # repeat the QAOA layer two times
    qml.layer(qaoa_layer, 2, params[0], params[1])

dev = qml.device('default.qubit', wires=len(wires))
cost_function = qml.VQECost(ansatz, cost_h, dev)
```
Added an ApproxTimeEvolution template to the PennyLane templates module, which can be used to implement Trotterized time-evolution under a Hamiltonian. (#710)

Added a qml.layer template-constructing function, which takes a unitary, and repeatedly applies it on a set of wires to a given depth. (#723)

def subroutine():
    qml.Hadamard(wires=[0])
    qml.CNOT(wires=[0, 1])
    qml.PauliX(wires=[1])

dev = qml.device('default.qubit', wires=3)

@qml.qnode(dev)
def circuit():
    qml.layer(subroutine, 3)
    return [qml.expval(qml.PauliZ(0)), qml.expval(qml.PauliZ(1))]

This creates the following circuit:

>>> circuit()
>>> print(circuit.draw())
0: ──H──╭C──X──H──╭C──X──H──╭C──X──┤ ⟨Z⟩
1: ─────╰X────────╰X────────╰X─────┤ ⟨Z⟩

Added the qml.utils.decompose_hamiltonian function. This function can be used to decompose a Hamiltonian into a linear combination of Pauli operators. (#671)

>>> A = np.array(
... [[-2, -2+1j, -2, -2],
... [-2-1j,  0,  0, -1],
... [-2,  0, -2, -1],
... [-2, -1, -1,  0]])
>>> coeffs, obs_list = decompose_hamiltonian(A)

New device features

It is now possible to specify custom wire labels, such as ['anc1', 'anc2', 0, 1, 3], where the labels can be strings or numbers. (#666)

Custom wire labels are defined by passing a list to the wires argument when creating the device:
```
>>> dev = qml.device("default.qubit", wires=['anc1', 'anc2', 0, 1, 3])
```
Quantum operations should then be invoked with these custom wire labels:
```
>>> @qml.qnode(dev)
>>> def circuit():
...    qml.Hadamard(wires='anc2')
...    qml.CNOT(wires=['anc1', 3])
...    ...
```
The existing behaviour, in which the number of wires is specified on device initialization, continues to work as usual. This gives a default behaviour where wires are labelled by consecutive integers.
```
>>> dev = qml.device("default.qubit", wires=5)
```
An integrated device test suite has been added, which can be used to run basic integration tests on core or external devices. (#695) (#724) (#733)

The test can be invoked against a particular device by calling the pl-device-test command line program:
```
$ pl-device-test --device=default.qubit --shots=1234 --analytic=False
```
If the tests are run on external devices, the device and its dependencies must be installed locally. For more details, please see the plugin test documentation.

Improvements

The functions implementing the quantum circuits building the Unitary Coupled-Cluster (UCCSD) VQE ansatz have been improved, with a more consistent naming convention and improved docstrings. (#748)

The changes include:
- The terms 1particle-1hole (ph) and 2particle-2hole (pphh) excitations were replaced with the names single and double excitations, respectively.
- The non-differentiable arguments in the UCCSD template were renamed accordingly: ph → s_wires, pphh → d_wires
- The term virtual, previously used to refer the unoccupied orbitals, was discarded.
- The Usage Details sections were updated and improved.
Added support for TensorFlow 2.3 and PyTorch 1.6. (#725)

Returning probabilities is now supported from photonic QNodes. As with qubit QNodes, photonic QNodes returning probabilities are end-to-end differentiable. (#699)

>>> dev = qml.device("strawberryfields.fock", wires=2, cutoff_dim=5)
>>> @qml.qnode(dev)
... def circuit(a):
...     qml.Displacement(a, 0, wires=0)
...     return qml.probs(wires=0)
>>> print(circuit(0.5))
[7.78800783e-01 1.94700196e-01 2.43375245e-02 2.02812704e-03 1.26757940e-04]

Breaking changes

The pennylane.plugins and pennylane.beta.plugins folders have been renamed to pennylane.devices and pennylane.beta.devices, to reflect their content better. (#726)

Bug fixes

The PennyLane interface conversion functions can now convert QNodes with pre-existing interfaces. (#707)

Documentation

The interfaces section of the documentation has been renamed to 'Interfaces and training', and updated with the latest variable handling details. (#753)

Contributors

This release contains contributions from (in alphabetical order):

Juan Miguel Arrazola, Thomas Bromley, Jack Ceroni, Alain Delgado Gran, Shadab Hussain, Theodor Isacsson, Josh Izaac, Nathan Killoran, Maria Schuld, Antal Száva, Nicola Vitucci.

Release 0.10.0

New features since last release

New and improved simulators

Added a new device, default.qubit.tf, a pure-state qubit simulator written using TensorFlow. As a result, it supports classical backpropagation as a means to compute the Jacobian. This can be faster than the parameter-shift rule for computing quantum gradients when the number of parameters to be optimized is large.

default.qubit.tf is designed to be used with end-to-end classical backpropagation (diff_method="backprop") with the TensorFlow interface. This is the default method of differentiation when creating a QNode with this device.

Using this method, the created QNode is a 'white-box' that is tightly integrated with your TensorFlow computation, including AutoGraph support:
```
>>> dev = qml.device("default.qubit.tf", wires=1)
>>> @tf.function
... @qml.qnode(dev, interface="tf", diff_method="backprop")
... def circuit(x):
...     qml.RX(x[1], wires=0)
...     qml.Rot(x[0], x[1], x[2], wires=0)
...     return qml.expval(qml.PauliZ(0))
>>> weights = tf.Variable([0.2, 0.5, 0.1])
>>> with tf.GradientTape() as tape:
...     res = circuit(weights)
>>> print(tape.gradient(res, weights))
tf.Tensor([-2.2526717e-01 -1.0086454e+00  1.3877788e-17], shape=(3,), dtype=float32)
```
See the default.qubit.tf documentation for more details.
The default.tensor plugin has been significantly upgraded. It now allows two different tensor network representations to be used: "exact" and "mps". The former uses a exact factorized representation of quantum states, while the latter uses a matrix product state representation. (#572) (#599)

New machine learning functionality and integrations

PennyLane QNodes can now be converted into Torch layers, allowing for creation of quantum and hybrid models using the torch.nn API. (#588)

A PennyLane QNode can be converted into a torch.nn layer using the qml.qnn.TorchLayer class:

>>> @qml.qnode(dev)
... def qnode(inputs, weights_0, weight_1):
...    # define the circuit
...    # ...

>>> weight_shapes = {"weights_0": 3, "weight_1": 1}
>>> qlayer = qml.qnn.TorchLayer(qnode, weight_shapes)

A hybrid model can then be easily constructed:

>>> model = torch.nn.Sequential(qlayer, torch.nn.Linear(2, 2))

Added a new "reversible" differentiation method which can be used in simulators, but not hardware.

The reversible approach is similar to backpropagation, but trades off extra computation for enhanced memory efficiency. Where backpropagation caches the state tensors at each step during a simulated evolution, the reversible method only caches the final pre-measurement state.

Compared to the parameter-shift method, the reversible method can be faster or slower, depending on the density and location of parametrized gates in a circuit (circuits with higher density of parametrized gates near the end of the circuit will see a benefit). (#670)
```
>>> dev = qml.device("default.qubit", wires=2)
... @qml.qnode(dev, diff_method="reversible")
... def circuit(x):
...     qml.RX(x, wires=0)
...     qml.RX(x, wires=0)
...     qml.CNOT(wires=[0,1])
...     return qml.expval(qml.PauliZ(0))
>>> qml.grad(circuit)(0.5)
(array(-0.47942554),)
```

New templates and cost functions

Added the new templates UCCSD, SingleExcitationUnitary, andDoubleExcitationUnitary, which together implement the Unitary Coupled-Cluster Singles and Doubles (UCCSD) ansatz to perform VQE-based quantum chemistry simulations using PennyLane-QChem. (#622) (#638) (#654) (#659) (#622)
Added module pennylane.qnn.cost with class SquaredErrorLoss. The module contains classes to calculate losses and cost functions on circuits with trainable parameters. (#642)

Improvements

Improves the wire management by making the Operator.wires attribute a wires object. (#666)
A significant improvement with respect to how QNodes and interfaces mark quantum function arguments as differentiable when using Autograd, designed to improve performance and make QNodes more intuitive. (#648) (#650)

In particular, the following changes have been made:
- A new ndarray subclass pennylane.numpy.tensor, which extends NumPy arrays with the keyword argument and attribute requires_grad. Tensors which have requires_grad=False are treated as non-differentiable by the Autograd interface.
- A new subpackage pennylane.numpy, which wraps autograd.numpy such that NumPy functions accept the requires_grad keyword argument, and allows Autograd to differentiate pennylane.numpy.tensor objects.
- The argnum argument to qml.grad is now optional; if not provided, arguments explicitly marked as requires_grad=False are excluded for the list of differentiable arguments. The ability to pass argnum has been retained for backwards compatibility, and if present the old behaviour persists.
The QNode Torch interface now inspects QNode positional arguments. If any argument does not have the attribute requires_grad=True, it is automatically excluded from quantum gradient computations. (#652) (#660)
The QNode TF interface now inspects QNode positional arguments. If any argument is not being watched by a tf.GradientTape(), it is automatically excluded from quantum gradient computations. (#655) (#660)
QNodes have two new public methods: QNode.set_trainable_args() and QNode.get_trainable_args(). These are designed to be called by interfaces, to specify to the QNode which of its input arguments are differentiable. Arguments which are non-differentiable will not be converted to PennyLane Variable objects within the QNode. (#660)
Added decomposition method to PauliX, PauliY, PauliZ, S, T, Hadamard, and PhaseShift gates, which decomposes each of these gates into rotation gates. (#668)
The CircuitGraph class now supports serializing contained circuit operations and measurement basis rotations to an OpenQASM2.0 script via the new CircuitGraph.to_openqasm() method. (#623)

Breaking changes

Removes support for Python 3.5. (#639)

Documentation

Various small typos were fixed.

Contributors

This release contains contributions from (in alphabetical order):

Thomas Bromley, Jack Ceroni, Alain Delgado Gran, Theodor Isacsson, Josh Izaac, Nathan Killoran, Maria Schuld, Antal Száva, Nicola Vitucci.

Release 0.9.0

New features since last release

New machine learning integrations

PennyLane QNodes can now be converted into Keras layers, allowing for creation of quantum and hybrid models using the Keras API. (#529)

A PennyLane QNode can be converted into a Keras layer using the KerasLayer class:

from pennylane.qnn import KerasLayer

@qml.qnode(dev)
def circuit(inputs, weights_0, weight_1):
   # define the circuit
   # ...

weight_shapes = {"weights_0": 3, "weight_1": 1}
qlayer = qml.qnn.KerasLayer(circuit, weight_shapes, output_dim=2)

A hybrid model can then be easily constructed:

model = tf.keras.models.Sequential([qlayer, tf.keras.layers.Dense(2)])

Added a new type of QNode, qml.qnodes.PassthruQNode. For simulators which are coded in an external library which supports automatic differentiation, PennyLane will treat a PassthruQNode as a "white box", and rely on the external library to directly provide gradients via backpropagation. This can be more efficient than the using parameter-shift rule for a large number of parameters. (#488)

Currently this behaviour is supported by PennyLane's default.tensor.tf device backend, compatible with the 'tf' interface using TensorFlow 2:
```
dev = qml.device('default.tensor.tf', wires=2)

@qml.qnode(dev, diff_method="backprop")
def circuit(params):
    qml.RX(params[0], wires=0)
    qml.RX(params[1], wires=1)
    qml.CNOT(wires=[0, 1])
    return qml.expval(qml.PauliZ(0))

qnode = PassthruQNode(circuit, dev)
params = tf.Variable([0.3, 0.1])

with tf.GradientTape() as tape:
    tape.watch(params)
    res = qnode(params)

grad = tape.gradient(res, params)
```

New optimizers

Added the qml.RotosolveOptimizer, a gradient-free optimizer that minimizes the quantum function by updating each parameter, one-by-one, via a closed-form expression while keeping other parameters fixed. (#636) (#539)
Added the qml.RotoselectOptimizer, which uses Rotosolve to minimizes a quantum function with respect to both the rotation operations applied and the rotation parameters. (#636) (#539)

For example, given a quantum function f that accepts parameters x and a list of corresponding rotation operations generators, the Rotoselect optimizer will, at each step, update both the parameter values and the list of rotation gates to minimize the loss:
```
>>> opt = qml.optimize.RotoselectOptimizer()
>>> x = [0.3, 0.7]
>>> generators = [qml.RX, qml.RY]
>>> for _ in range(100):
...     x, generators = opt.step(f, x, generators)
```

New operations

Added the PauliRot gate, which performs an arbitrary Pauli rotation on multiple qubits, and the MultiRZ gate, which performs a rotation generated by a tensor product of Pauli Z operators. (#559)

dev = qml.device('default.qubit', wires=4)

@qml.qnode(dev)
def circuit(angle):
    qml.PauliRot(angle, "IXYZ", wires=[0, 1, 2, 3])
    return [qml.expval(qml.PauliZ(wire)) for wire in [0, 1, 2, 3]]

>>> circuit(0.4)
[1.         0.92106099 0.92106099 1.        ]
>>> print(circuit.draw())
 0: ──╭RI(0.4)──┤ ⟨Z⟩
 1: ──├RX(0.4)──┤ ⟨Z⟩
 2: ──├RY(0.4)──┤ ⟨Z⟩
 3: ──╰RZ(0.4)──┤ ⟨Z⟩

If the PauliRot gate is not supported on the target device, it will be decomposed into Hadamard, RX and MultiRZ gates. Note that identity gates in the Pauli word result in untouched wires:

>>> print(circuit.draw())
 0: ───────────────────────────────────┤ ⟨Z⟩
 1: ──H──────────╭RZ(0.4)──H───────────┤ ⟨Z⟩
 2: ──RX(1.571)──├RZ(0.4)──RX(-1.571)──┤ ⟨Z⟩
 3: ─────────────╰RZ(0.4)──────────────┤ ⟨Z⟩

If the MultiRZ gate is not supported, it will be decomposed into CNOT and RZ gates:

>>> print(circuit.draw())
 0: ──────────────────────────────────────────────────┤ ⟨Z⟩
 1: ──H──────────────╭X──RZ(0.4)──╭X──────H───────────┤ ⟨Z⟩
 2: ──RX(1.571)──╭X──╰C───────────╰C──╭X──RX(-1.571)──┤ ⟨Z⟩
 3: ─────────────╰C───────────────────╰C──────────────┤ ⟨Z⟩

PennyLane now provides DiagonalQubitUnitary for diagonal gates, that are e.g., encountered in IQP circuits. These kinds of gates can be evaluated much faster on a simulator device. (#567)

The gate can be used, for example, to efficiently simulate oracles:

dev = qml.device('default.qubit', wires=3)

# Function as a bitstring
f = np.array([1, 0, 0, 1, 1, 0, 1, 0])

@qml.qnode(dev)
def circuit(weights1, weights2):
    qml.templates.StronglyEntanglingLayers(weights1, wires=[0, 1, 2])

    # Implements the function as a phase-kickback oracle
    qml.DiagonalQubitUnitary((-1)**f, wires=[0, 1, 2])

    qml.templates.StronglyEntanglingLayers(weights2, wires=[0, 1, 2])
    return [qml.expval(qml.PauliZ(w)) for w in range(3)]

Added the TensorN CVObservable that can represent the tensor product of the NumberOperator on photonic backends. (#608)

New templates

Added the ArbitraryUnitary and ArbitraryStatePreparation templates, which use PauliRot gates to perform an arbitrary unitary and prepare an arbitrary basis state with the minimal number of parameters. (#590)

dev = qml.device('default.qubit', wires=3)

@qml.qnode(dev)
def circuit(weights1, weights2):
      qml.templates.ArbitraryStatePreparation(weights1, wires=[0, 1, 2])
      qml.templates.ArbitraryUnitary(weights2, wires=[0, 1, 2])
      return qml.probs(wires=[0, 1, 2])

Added the IQPEmbedding template, which encodes inputs into the diagonal gates of an IQP circuit. (#605)
Added the SimplifiedTwoDesign template, which implements the circuit design of Cerezo et al. (2020). (#556)
Added the BasicEntanglerLayers template, which is a simple layer architecture of rotations and CNOT nearest-neighbour entanglers. (#555)

PennyLane now offers a broadcasting function to easily construct templates: qml.broadcast() takes single quantum operations or other templates and applies them to wires in a specific pattern. (#515) (#522) (#526) (#603)

For example, we can use broadcast to repeat a custom template across multiple wires:

from pennylane.templates import template

@template
def mytemplate(pars, wires):
    qml.Hadamard(wires=wires)
    qml.RY(pars, wires=wires)

dev = qml.device('default.qubit', wires=3)

@qml.qnode(dev)
def circuit(pars):
    qml.broadcast(mytemplate, pattern="single", wires=[0,1,2], parameters=pars)
    return qml.expval(qml.PauliZ(0))

>>> circuit([1, 1, 0.1])
-0.841470984807896
>>> print(circuit.draw())
 0: ──H──RY(1.0)──┤ ⟨Z⟩
 1: ──H──RY(1.0)──┤
 2: ──H──RY(0.1)──┤

For other available patterns, see the broadcast function documentation.

Breaking changes

The QAOAEmbedding now uses the new MultiRZ gate as a ZZ entangler, which changes the convention. While previously, the ZZ gate in the embedding was implemented as
```
CNOT(wires=[wires[0], wires[1]])
RZ(2 * parameter, wires=wires[0])
CNOT(wires=[wires[0], wires[1]])
```
the MultiRZ corresponds to
```
CNOT(wires=[wires[1], wires[0]])
RZ(parameter, wires=wires[0])
CNOT(wires=[wires[1], wires[0]])
```
which differs in the factor of 2, and fixes a bug in the wires that the CNOT was applied to. (#609)
Probability methods are handled by QubitDevice and device method requirements are modified to simplify plugin development. (#573)
The internal variables All and Any to mark an Operation as acting on all or any wires have been renamed to AllWires and AnyWires. (#614)

Improvements

A new Wires class was introduced for the internal bookkeeping of wire indices. (#615)
Improvements to the speed/performance of the default.qubit device. (#567) (#559)
Added the "backprop" and "device" differentiation methods to the qnode decorator. (#552)
- "backprop": Use classical backpropagation. Default on simulator devices that are classically end-to-end differentiable. The returned QNode can only be used with the same machine learning framework (e.g., default.tensor.tf simulator with the tensorflow interface).
- "device": Queries the device directly for the gradient.
Using the "backprop" differentiation method with the default.tensor.tf device, the created QNode is a 'white-box', and is tightly integrated with the overall TensorFlow computation:
```
>>> dev = qml.device("default.tensor.tf", wires=1)
>>> @qml.qnode(dev, interface="tf", diff_method="backprop")
>>> def circuit(x):
...     qml.RX(x[1], wires=0)
...     qml.Rot(x[0], x[1], x[2], wires=0)
...     return qml.expval(qml.PauliZ(0))
>>> vars = tf.Variable([0.2, 0.5, 0.1])
>>> with tf.GradientTape() as tape:
...     res = circuit(vars)
>>> tape.gradient(res, vars)
<tf.Tensor: shape=(3,), dtype=float32, numpy=array([-2.2526717e-01, -1.0086454e+00,  1.3877788e-17], dtype=float32)>
```

The circuit drawer now displays inverted operations, as well as wires where probabilities are returned from the device: (#540)

>>> @qml.qnode(dev)
... def circuit(theta):
...     qml.RX(theta, wires=0)
...     qml.CNOT(wires=[0, 1])
...     qml.S(wires=1).inv()
...     return qml.probs(wires=[0, 1])
>>> circuit(0.2)
array([0.99003329, 0.        , 0.        , 0.00996671])
>>> print(circuit.draw())
0: ──RX(0.2)──╭C───────╭┤ Probs
1: ───────────╰X──S⁻¹──╰┤ Probs

You can now evaluate the metric tensor of a VQE Hamiltonian via the new VQECost.metric_tensor method. This allows VQECost objects to be directly optimized by the quantum natural gradient optimizer (qml.QNGOptimizer). (#618)
The input check functions in pennylane.templates.utils are now public and visible in the API documentation. (#566)
Added keyword arguments for step size and order to the qnode decorator, as well as the QNode and JacobianQNode classes. This enables the user to set the step size and order when using finite difference methods. These options are also exposed when creating QNode collections. (#530) (#585) (#587)
The decomposition for the CRY gate now uses the simpler form RY @ CNOT @ RY @ CNOT (#547)
The underlying queuing system was refactored, removing the qml._current_context property that held the currently active QNode or OperationRecorder. Now, all objects that expose a queue for operations inherit from QueuingContext and register their queue globally. (#548)
The PennyLane repository has a new benchmarking tool which supports the comparison of different git revisions. (#568) (#560) (#516)

Documentation

Updated the development section by creating a landing page with links to sub-pages containing specific guides. (#596)
Extended the developer's guide by a section explaining how to add new templates. (#564)

Bug fixes

tf.GradientTape().jacobian() can now be evaluated on QNodes using the TensorFlow interface. (#626)
RandomLayers() is now compatible with the qiskit devices. (#597)
DefaultQubit.probability() now returns the correct probability when called with device.analytic=False. (#563)
Fixed a bug in the StronglyEntanglingLayers template, allowing it to work correctly when applied to a single wire. (544)
Fixed a bug when inverting operations with decompositions; operations marked as inverted are now correctly inverted when the fallback decomposition is called. (#543)
The QNode.print_applied() method now correctly displays wires where qml.prob() is being returned. #542

Contributors

This release contains contributions from (in alphabetical order):

Ville Bergholm, Lana Bozanic, Thomas Bromley, Theodor Isacsson, Josh Izaac, Nathan Killoran, Maggie Li, Johannes Jakob Meyer, Maria Schuld, Sukin Sim, Antal Száva.

Release 0.8.1

Improvements

Beginning of support for Python 3.8, with the test suite now being run in a Python 3.8 environment. (#501)

Documentation

Present templates as a gallery of thumbnails showing the basic circuit architecture. (#499)

Bug fixes

Fixed a bug where multiplying a QNode parameter by 0 caused a divide by zero error when calculating the parameter shift formula. (#512)
Fixed a bug where the shape of differentiable QNode arguments was being cached on the first construction, leading to indexing errors if the QNode was re-evaluated if the argument changed shape. (#505)

Contributors

This release contains contributions from (in alphabetical order):

Ville Bergholm, Josh Izaac, Johannes Jakob Meyer, Maria Schuld, Antal Száva.

Release 0.8.0

New features since last release

Added a quantum chemistry package, pennylane.qchem, which supports integration with OpenFermion, Psi4, PySCF, and OpenBabel. (#453)

Features include:
- Generate the qubit Hamiltonians directly starting with the atomic structure of the molecule.
- Calculate the mean-field (Hartree-Fock) electronic structure of molecules.
- Allow to define an active space based on the number of active electrons and active orbitals.
- Perform the fermionic-to-qubit transformation of the electronic Hamiltonian by using different functions implemented in OpenFermion.
- Convert OpenFermion's QubitOperator to a Pennylane Hamiltonian class.
- Perform a Variational Quantum Eigensolver (VQE) computation with this Hamiltonian in PennyLane.
Check out the quantum chemistry quickstart, as well the quantum chemistry and VQE tutorials.
PennyLane now has some functions and classes for creating and solving VQE problems. (#467)
- qml.Hamiltonian: a lightweight class for representing qubit Hamiltonians
- qml.VQECost: a class for quickly constructing a differentiable cost function given a circuit ansatz, Hamiltonian, and one or more devices
```
>>> H = qml.vqe.Hamiltonian(coeffs, obs)
>>> cost = qml.VQECost(ansatz, hamiltonian, dev, interface="torch")
>>> params = torch.rand([4, 3])
>>> cost(params)
tensor(0.0245, dtype=torch.float64)
```

Added a circuit drawing feature that provides a text-based representation of a QNode instance. It can be invoked via qnode.draw(). The user can specify to display variable names instead of variable values and choose either an ASCII or Unicode charset. (#446)

Consider the following circuit as an example:

@qml.qnode(dev)
def qfunc(a, w):
    qml.Hadamard(0)
    qml.CRX(a, wires=[0, 1])
    qml.Rot(w[0], w[1], w[2], wires=[1])
    qml.CRX(-a, wires=[0, 1])

    return qml.expval(qml.PauliZ(0) @ qml.PauliZ(1))

We can draw the circuit after it has been executed:

>>> result = qfunc(2.3, [1.2, 3.2, 0.7])
>>> print(qfunc.draw())
 0: ──H──╭C────────────────────────────╭C─────────╭┤ ⟨Z ⊗ Z⟩
 1: ─────╰RX(2.3)──Rot(1.2, 3.2, 0.7)──╰RX(-2.3)──╰┤ ⟨Z ⊗ Z⟩
>>> print(qfunc.draw(charset="ascii"))
 0: --H--+C----------------------------+C---------+| <Z @ Z>
 1: -----+RX(2.3)--Rot(1.2, 3.2, 0.7)--+RX(-2.3)--+| <Z @ Z>
>>> print(qfunc.draw(show_variable_names=True))
 0: ──H──╭C─────────────────────────────╭C─────────╭┤ ⟨Z ⊗ Z⟩
 1: ─────╰RX(a)──Rot(w[0], w[1], w[2])──╰RX(-1*a)──╰┤ ⟨Z ⊗ Z⟩

Added QAOAEmbedding and its parameter initialization as a new trainable template. (#442)
Added the qml.probs() measurement function, allowing QNodes to differentiate variational circuit probabilities on simulators and hardware. (#432)
```
@qml.qnode(dev)
def circuit(x):
    qml.Hadamard(wires=0)
    qml.RY(x, wires=0)
    qml.RX(x, wires=1)
    qml.CNOT(wires=[0, 1])
    return qml.probs(wires=[0])
```
Executing this circuit gives the marginal probability of wire 1:
```
>>> circuit(0.2)
[0.40066533 0.59933467]
```
QNodes that return probabilities fully support autodifferentiation.
Added the convenience load functions qml.from_pyquil, qml.from_quil and qml.from_quil_file that convert pyQuil objects and Quil code to PennyLane templates. This feature requires version 0.8 or above of the PennyLane-Forest plugin. (#459)

Added a qml.inv method that inverts templates and sequences of Operations. Added a @qml.template decorator that makes templates return the queued Operations. (#462)

For example, using this function to invert a template inside a QNode:

    @qml.template
    def ansatz(weights, wires):
        for idx, wire in enumerate(wires):
            qml.RX(weights[idx], wires=[wire])

        for idx in range(len(wires) - 1):
            qml.CNOT(wires=[wires[idx], wires[idx + 1]])

    dev = qml.device('default.qubit', wires=2)

    @qml.qnode(dev)
    def circuit(weights):
        qml.inv(ansatz(weights, wires=[0, 1]))
        return qml.expval(qml.PauliZ(0) @ qml.PauliZ(1))

Added the QNodeCollection container class, that allows independent QNodes to be stored and evaluated simultaneously. Experimental support for asynchronous evaluation of contained QNodes is provided with the parallel=True keyword argument. (#466)

Added a high level qml.map function, that maps a quantum circuit template over a list of observables or devices, returning a QNodeCollection. (#466)

For example:

>>> def my_template(params, wires, **kwargs):
>>>    qml.RX(params[0], wires=wires[0])
>>>    qml.RX(params[1], wires=wires[1])
>>>    qml.CNOT(wires=wires)

>>> obs_list = [qml.PauliX(0) @ qml.PauliZ(1), qml.PauliZ(0) @ qml.PauliX(1)]
>>> dev = qml.device("default.qubit", wires=2)
>>> qnodes = qml.map(my_template, obs_list, dev, measure="expval")
>>> qnodes([0.54, 0.12])
array([-0.06154835  0.99280864])

Added high level qml.sum, qml.dot, qml.apply functions that act on QNode collections. (#466)

qml.apply allows vectorized functions to act over the entire QNode collection:
```
>>> qnodes = qml.map(my_template, obs_list, dev, measure="expval")
>>> cost = qml.apply(np.sin, qnodes)
>>> cost([0.54, 0.12])
array([-0.0615095  0.83756375])
```
qml.sum and qml.dot take the sum of a QNode collection, and a dot product of tensors/arrays/QNode collections, respectively.

Breaking changes

Deprecated the old-style QNode such that only the new-style QNode and its syntax can be used, moved all related files from the pennylane/beta folder to pennylane. (#440)

Improvements

Added the Tensor.prune() method and the Tensor.non_identity_obs property for extracting non-identity instances from the observables making up a Tensor instance. (#498)
Renamed the expt.tensornet and expt.tensornet.tf devices to default.tensor and default.tensor.tf. (#495)
Added a serialization method to the CircuitGraph class that is used to create a unique hash for each quantum circuit graph. (#470)
Added the Observable.eigvals method to return the eigenvalues of observables. (#449)
Added the Observable.diagonalizing_gates method to return the gates that diagonalize an observable in the computational basis. (#454)
Added the Operator.matrix method to return the matrix representation of an operator in the computational basis. (#454)
Added a QubitDevice class which implements common functionalities of plugin devices such that plugin devices can rely on these implementations. The new QubitDevice also includes a new execute method, which allows for more convenient plugin design. In addition, QubitDevice also unifies the way samples are generated on qubit-based devices. (#452) (#473)
Improved documentation of AmplitudeEmbedding and BasisEmbedding templates. (#441) (#439)
Codeblocks in the documentation now have a 'copy' button for easily copying examples. (#437)

Documentation

Update the developers plugin guide to use QubitDevice. (#483)

Bug fixes

Fixed a bug in CVQNode._pd_analytic, where non-descendant observables were not Heisenberg-transformed before evaluating the partial derivatives when using the order-2 parameter-shift method, resulting in an erroneous Jacobian for some circuits. (#433)

Contributors

This release contains contributions from (in alphabetical order):

Juan Miguel Arrazola, Ville Bergholm, Alain Delgado Gran, Olivia Di Matteo, Theodor Isacsson, Josh Izaac, Soran Jahangiri, Nathan Killoran, Johannes Jakob Meyer, Zeyue Niu, Maria Schuld, Antal Száva.

Release 0.7.0

New features since last release

Custom padding constant in AmplitudeEmbedding is supported (see 'Breaking changes'.) (#419)
StronglyEntanglingLayer and RandomLayer now work with a single wire. (#409) (#413)
Added support for applying the inverse of an Operation within a circuit. (#377)
Added an OperationRecorder() context manager, that allows templates and quantum functions to be executed while recording events. The recorder can be used with and without QNodes as a debugging utility. (#388)
Operations can now specify a decomposition that is used when the desired operation is not supported on the target device. (#396)
The ability to load circuits from external frameworks as templates has been added via the new qml.load() function. This feature requires plugin support --- this initial release provides support for Qiskit circuits and QASM files when pennylane-qiskit is installed, via the functions qml.from_qiskit and qml.from_qasm. (#418)
An experimental tensor network device has been added (#416) (#395) (#394) (#380)
An experimental tensor network device which uses TensorFlow for backpropagation has been added (#427)
Custom padding constant in AmplitudeEmbedding is supported (see 'Breaking changes'.) (#419)

Breaking changes

The pad parameter in AmplitudeEmbedding() is now either None (no automatic padding), or a number that is used as the padding constant. (#419)
Initialization functions now return a single array of weights per function. Utilities for multi-weight templates Interferometer() and CVNeuralNetLayers() are provided. (#412)
The single layer templates RandomLayer(), CVNeuralNetLayer() and StronglyEntanglingLayer() have been turned into private functions _random_layer(), _cv_neural_net_layer() and _strongly_entangling_layer(). Recommended use is now via the corresponding Layers() templates. (#413)

Improvements

Added extensive input checks in templates. (#419)
Templates integration tests are rewritten - now cover keyword/positional argument passing, interfaces and combinations of templates. (#409) (#419)
State vector preparation operations in the default.qubit plugin can now be applied to subsets of wires, and are restricted to being the first operation in a circuit. (#346)
The QNode class is split into a hierarchy of simpler classes. (#354) (#398) (#415) (#417) (#425)
Added the gates U1, U2 and U3 parametrizing arbitrary unitaries on 1, 2 and 3 qubits and the Toffoli gate to the set of qubit operations. (#396)
Changes have been made to accomodate the movement of the main function in pytest._internal to pytest._internal.main in pip 19.3. (#404)
Added the templates BasisStatePreparation and MottonenStatePreparation that use gates to prepare a basis state and an arbitrary state respectively. (#336)
Added decompositions for BasisState and QubitStateVector based on state preparation templates. (#414)
Replaces the pseudo-inverse in the quantum natural gradient optimizer (which can be numerically unstable) with np.linalg.solve. (#428)

Contributors

This release contains contributions from (in alphabetical order):

Ville Bergholm, Josh Izaac, Nathan Killoran, Angus Lowe, Johannes Jakob Meyer, Oluwatobi Ogunbayo, Maria Schuld, Antal Száva.

Release 0.6.1

New features since last release

Added a print_applied method to QNodes, allowing the operation and observable queue to be printed as last constructed. (#378)

Improvements

A new Operator base class is introduced, which is inherited by both the Observable class and the Operation class. (#355)
Removed deprecated @abstractproperty decorators in _device.py. (#374)
The CircuitGraph class is updated to deal with Operation instances directly. (#344)
Comprehensive gradient tests have been added for the interfaces. (#381)

Documentation

The new restructured documentation has been polished and updated. (#387) (#375) (#372) (#370) (#369) (#367) (#364)
Updated the development guides. (#382) (#379)
Added all modules, classes, and functions to the API section in the documentation. (#373)

Bug fixes

Replaces the existing np.linalg.norm normalization with hand-coded normalization, allowing AmplitudeEmbedding to be used with differentiable parameters. AmplitudeEmbedding tests have been added and improved. (#376)

Contributors

This release contains contributions from (in alphabetical order):

Ville Bergholm, Josh Izaac, Nathan Killoran, Maria Schuld, Antal Száva

Release 0.6.0

New features since last release

The devices default.qubit and default.gaussian have a new initialization parameter analytic that indicates if expectation values and variances should be calculated analytically and not be estimated from data. (#317)
Added C-SWAP gate to the set of qubit operations (#330)
The TensorFlow interface has been renamed from "tfe" to "tf", and now supports TensorFlow 2.0. (#337)
Added the S and T gates to the set of qubit operations. (#343)
Tensor observables are now supported within the expval, var, and sample functions, by using the @ operator. (#267)

Breaking changes

The argument n specifying the number of samples in the method Device.sample was removed. Instead, the method will always return Device.shots many samples. (#317)

Improvements

The number of shots / random samples used to estimate expectation values and variances, Device.shots, can now be changed after device creation. (#317)
Unified import shortcuts to be under qml in qnode.py and test_operation.py (#329)
The quantum natural gradient now uses scipy.linalg.pinvh which is more efficient for symmetric matrices than the previously used scipy.linalg.pinv. (#331)
The deprecated qml.expval.Observable syntax has been removed. (#267)
Remainder of the unittest-style tests were ported to pytest. (#310)
The do_queue argument for operations now only takes effect within QNodes. Outside of QNodes, operations can now be instantiated without needing to specify do_queue. (#359)

Documentation

The docs are rewritten and restructured to contain a code introduction section as well as an API section. (#314)
Added Ising model example to the tutorials (#319)
Added tutorial for QAOA on MaxCut problem (#328)
Added QGAN flow chart figure to its tutorial (#333)
Added missing figures for gallery thumbnails of state-preparation and QGAN tutorials (#326)
Fixed typos in the state preparation tutorial (#321)
Fixed bug in VQE tutorial 3D plots (#327)

Bug fixes

Fixed typo in measurement type error message in qnode.py (#341)

Contributors

This release contains contributions from (in alphabetical order):

Shahnawaz Ahmed, Ville Bergholm, Aroosa Ijaz, Josh Izaac, Nathan Killoran, Angus Lowe, Johannes Jakob Meyer, Maria Schuld, Antal Száva, Roeland Wiersema.

Release 0.5.0

New features since last release

Adds a new optimizer, qml.QNGOptimizer, which optimizes QNodes using quantum natural gradient descent. See https://arxiv.org/abs/1909.02108 for more details. (#295) (#311)
Adds a new QNode method, QNode.metric_tensor(), which returns the block-diagonal approximation to the Fubini-Study metric tensor evaluated on the attached device. (#295)
Sampling support: QNodes can now return a specified number of samples from a given observable via the top-level pennylane.sample() function. To support this on plugin devices, there is a new Device.sample method.

Calculating gradients of QNodes that involve sampling is not possible. (#256)
default.qubit has been updated to provide support for sampling. (#256)
Added controlled rotation gates to PennyLane operations and default.qubit plugin. (#251)

Breaking changes

The method Device.supported was removed, and replaced with the methods Device.supports_observable and Device.supports_operation. Both methods can be called with string arguments (dev.supports_observable('PauliX')) and class arguments (dev.supports_observable(qml.PauliX)). (#276)
The following CV observables were renamed to comply with the new Operation/Observable scheme: MeanPhoton to NumberOperator, Homodyne to QuadOperator and NumberState to FockStateProjector. (#254)

Improvements

The AmplitudeEmbedding function now provides options to normalize and pad features to ensure a valid state vector is prepared. (#275)
Operations can now optionally specify generators, either as existing PennyLane operations, or by providing a NumPy array. (#295) (#313)
Adds a Device.parameters property, so that devices can view a dictionary mapping free parameters to operation parameters. This will allow plugin devices to take advantage of parametric compilation. (#283)
Introduces two enumerations: Any and All, representing any number of wires and all wires in the system respectively. They can be imported from pennylane.operation, and can be used when defining the Operation.num_wires class attribute of operations. (#277)

As part of this change:
- All is equivalent to the integer 0, for backwards compatibility with the existing test suite
- Any is equivalent to the integer -1 to allow numeric comparison operators to continue working
- An additional validation is now added to the Operation class, which will alert the user that an operation with num_wires = All is being incorrectly.
The one-qubit rotations in pennylane.plugins.default_qubit no longer depend on Scipy's expm. Instead they are calculated with Euler's formula. (#292)
Creates an ObservableReturnTypes enumeration class containing Sample, Variance and Expectation. These new values can be assigned to the return_type attribute of an Observable. (#290)
Changed the signature of the RandomLayer and RandomLayers templates to have a fixed seed by default. (#258)
setup.py has been cleaned up, removing the non-working shebang, and removing unused imports. (#262)

Documentation

A documentation refactor to simplify the tutorials and include Sphinx-Gallery. (#291)
- Examples and tutorials previously split across the examples/ and doc/tutorials/ directories, in a mixture of ReST and Jupyter notebooks, have been rewritten as Python scripts with ReST comments in a single location, the examples/ folder.
- Sphinx-Gallery is used to automatically build and run the tutorials. Rendered output is displayed in the Sphinx documentation.
- Links are provided at the top of every tutorial page for downloading the tutorial as an executable python script, downloading the tutorial as a Jupyter notebook, or viewing the notebook on GitHub.
- The tutorials table of contents have been moved to a single quick start page.
Fixed a typo in QubitStateVector. (#296)
Fixed a typo in the default_gaussian.gaussian_state function. (#293)
Fixed a typo in the gradient recipe within the RX, RY, RZ operation docstrings. (#248)
Fixed a broken link in the tutorial documentation, as a result of the qml.expval.Observable deprecation. (#246)

Bug fixes

Fixed a bug where a PolyXP observable would fail if applied to subsets of wires on default.gaussian. (#277)

Contributors

This release contains contributions from (in alphabetical order):

Simon Cross, Aroosa Ijaz, Josh Izaac, Nathan Killoran, Johannes Jakob Meyer, Rohit Midha, Nicolás Quesada, Maria Schuld, Antal Száva, Roeland Wiersema.

Release 0.4.0

New features since last release

pennylane.expval() is now a top-level function, and is no longer a package of classes. For now, the existing pennylane.expval.Observable interface continues to work, but will raise a deprecation warning. (#232)
Variance support: QNodes can now return the variance of observables, via the top-level pennylane.var() function. To support this on plugin devices, there is a new Device.var method.

The following observables support analytic gradients of variances:
- All qubit observables (requiring 3 circuit evaluations for involutory observables such as Identity, X, Y, Z; and 5 circuit evals for non-involutary observables, currently only qml.Hermitian)
- First-order CV observables (requiring 5 circuit evaluations)
Second-order CV observables support numerical variance gradients.
pennylane.about() function added, providing details on current PennyLane version, installed plugins, Python, platform, and NumPy versions (#186)
Removed the logic that allowed wires to be passed as a positional argument in quantum operations. This allows us to raise more useful error messages for the user if incorrect syntax is used. (#188)
Adds support for multi-qubit expectation values of the pennylane.Hermitian() observable (#192)
Adds support for multi-qubit expectation values in default.qubit. (#202)
Organize templates into submodules (#195). This included the following improvements:
- Distinguish embedding templates from layer templates.
- New random initialization functions supporting the templates available in the new submodule pennylane.init.
- Added a random circuit template (RandomLayers()), in which rotations and 2-qubit gates are randomly distributed over the wires
- Add various embedding strategies

Breaking changes

The Device methods expectations, pre_expval, and post_expval have been renamed to observables, pre_measure, and post_measure respectively. (#232)

Improvements

default.qubit plugin now uses np.tensordot when applying quantum operations and evaluating expectations, resulting in significant speedup (#239), (#241)
PennyLane now allows division of quantum operation parameters by a constant (#179)
Portions of the test suite are in the process of being ported to pytest. Note: this is still a work in progress.

Ported tests include:
- test_ops.py
- test_about.py
- test_classical_gradients.py
- test_observables.py
- test_measure.py
- test_init.py
- test_templates*.py
- test_ops.py
- test_variable.py
- test_qnode.py (partial)

Bug fixes

Fixed a bug in Device.supported, which would incorrectly mark an operation as supported if it shared a name with an observable (#203)
Fixed a bug in Operation.wires, by explicitly casting the type of each wire to an integer (#206)
Removed code in PennyLane which configured the logger, as this would clash with users' configurations (#208)
Fixed a bug in default.qubit, in which QubitStateVector operations were accidentally being cast to np.float instead of np.complex. (#211)

Contributors

This release contains contributions from:

Shahnawaz Ahmed, riveSunder, Aroosa Ijaz, Josh Izaac, Nathan Killoran, Maria Schuld.

Release 0.3.1

Bug fixes

Fixed a bug where the interfaces submodule was not correctly being packaged via setup.py

Release 0.3.0

New features since last release

PennyLane now includes a new interfaces submodule, which enables QNode integration with additional machine learning libraries.
Adds support for an experimental PyTorch interface for QNodes
Adds support for an experimental TensorFlow eager execution interface for QNodes
Adds a PyTorch+GPU+QPU tutorial to the documentation
Documentation now includes links and tutorials including the new PennyLane-Forest plugin.

Improvements

Printing a QNode object, via print(qnode) or in an interactive terminal, now displays more useful information regarding the QNode, including the device it runs on, the number of wires, it's interface, and the quantum function it uses:
```
>>> print(qnode)
<QNode: device='default.qubit', func=circuit, wires=2, interface=PyTorch>
```

Contributors

This release contains contributions from:

Josh Izaac and Nathan Killoran.

Release 0.2.0

New features since last release

Added the Identity expectation value for both CV and qubit models (#135)
Added the templates.py submodule, containing some commonly used QML models to be used as ansatz in QNodes (#133)
Added the qml.Interferometer CV operation (#152)
Wires are now supported as free QNode parameters (#151)
Added ability to update stepsizes of the optimizers (#159)

Improvements

Removed use of hardcoded values in the optimizers, made them parameters (see #131 and #132)
Created the new PlaceholderExpectation, to be used when both CV and qubit expval modules contain expectations with the same name
Provide a way for plugins to view the operation queue before applying operations. This allows for on-the-fly modifications of the queue, allowing hardware-based plugins to support the full range of qubit expectation values. (#143)
QNode return values now support any form of sequence, such as lists, sets, etc. (#144)
CV analytic gradient calculation is now more robust, allowing for operations which may not themselves be differentiated, but have a well defined _heisenberg_rep method, and so may succeed operations that are analytically differentiable (#152)

Bug fixes

Fixed a bug where the variational classifier example was not batching when learning parity (see #128 and #129)
Fixed an inconsistency where some initial state operations were documented as accepting complex parameters - all operations now accept real values (#146)

Contributors

This release contains contributions from:

Christian Gogolin, Josh Izaac, Nathan Killoran, and Maria Schuld.

Release 0.1.0

Initial public release.

Contributors

This release contains contributions from:

Ville Bergholm, Josh Izaac, Maria Schuld, Christian Gogolin, and Nathan Killoran.

Files

CHANGELOG.md

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History

CHANGELOG.md

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Release 0.18.0-dev (development release)

New features since last release

Improvements

Breaking changes

Bug fixes

Documentation

Contributors

Release 0.17.0 (current release)

New features since the last release

Circuit optimization

QNodes are even more powerful

Device Resource Tracker

Containerization support

Improved Hamiltonian simulations

New gradients module

Even more new operations and templates

Improvements

Breaking changes

Bug fixes

Documentation

Contributors

Release 0.16.0

First class support for quantum kernels

Extract the fourier representation of quantum circuits

Seamless support for working with the Pauli group

New transforms

Extended QAOA module

Extended operations and templates

Improvements

Breaking changes

Bug fixes

Documentation

Contributors

Release 0.15.1

Bug fixes

Documentation

Contributors

Release 0.15.0

New features since last release

Better and more flexible shot control

New differentiable quantum transforms

More operations and templates

Support for higher-order derivatives on hardware

Improvements

Breaking changes

Bug fixes

Documentation

Contributors

Release 0.14.1

Bug fixes

Documentation

Contributors

Release 0.14.0

New features since last release

Perform quantum machine learning with JAX

New, faster, quantum gradient methods

More operations and templates

QNode transformations

A faster, leaner, and more flexible core

Improvements

Breaking changes

Bug fixes

Contributors

Release 0.13.0

New features since last release

Automatically optimize the number of measurements

New quantum gradient features

New operations, templates, and measurements

Estimate and track resources

Improvements

Breaking changes

Bug fixes

Contributors

Release 0.12.0