Diagonal gate

[bichengying]

Add an N-qubit DiagonalGate, which is specified in #3866. The decomposition algorithm (2^n-1 Rz gates and 2^n -2 CNOT gates) is implemented based on the paper:

Welch, Jonathan, et al. "Efficient quantum circuits for diagonal unitaries without ancillas." New Journal of Physics 16.3 (2014): 033040. https://iopscience.iop.org/article/10.1088/1367-2630/16/3/033040/meta

For the step-by-step explanation of the implemention, please refer this colab.

A current known issue is that the decomposition algorithm has a global phase shift between the diagonal unitary matrix and the decomposed circuit implementation. It can produce a surprising effect if the diagonal gates is used within a partial system, such as under the controlled gate. Hence, a GlobalPhaseOperation is added into the _decompose_ method. But GlobalPhaseOperation doesn't have as universal support as the single-/two-qubit gates. So adding GlobalPhaseOperation may limit the usage of DiagonalGate.

[vtomole]

Call the file and classes diagonal_gate instead of n_qubit_diagonal_gate.

[balopat]

Looking great, I found a bunch of nits though. +1 to renaming the file to diagonal_gate.py.

[bichengying]

Thanks for reviewing! The file has been renamed to diagonal_gate. About parameterized DiagonalGate comment I have another question. Please take a look again.

[balopat]

you can simplify these two lines to assert cirq.decompose(op) == [op]

[bichengying]

Done.

[balopat]

LGTM, great! One more tiny nit

[balopat]

One more thing: cirq.contrib.acquaintance.executor_test.py has a test DiagonalGate defined. Can you replace that with the new shiny DiagonalGate? Thanks!

[balopat]

One more thing: cirq.contrib.acquaintance.executor_test.py has a test DiagonalGate defined. Can you replace that with the new shiny DiagonalGate? Thanks!

[bichengying]

One more thing: cirq.contrib.acquaintance.executor_test.py has a test DiagonalGate defined. Can you replace that with the new shiny DiagonalGate? Thanks!

Sure. Done.

[daxfohl]

Over in qiskit they mention Hidden Shift can be represented by a diagonal gate https://qiskit.org/documentation/stubs/qiskit.circuit.library.Diagonal.html, but I'm not grokking. We have a hidden shift example https://github.com/quantumlib/Cirq/blob/master/examples/hidden_shift_algorithm.py. Should it be updated to use this (or perhaps Hamiltonian Binary since you mention they have the same underlying math)?

[bichengying]

Over in qiskit they mention Hidden Shift can be represented by a diagonal gate https://qiskit.org/documentation/stubs/qiskit.circuit.library.Diagonal.html, but I'm not grokking. We have a hidden shift example https://github.com/quantumlib/Cirq/blob/master/examples/hidden_shift_algorithm.py. Should it be updated to use this (or perhaps Hamiltonian Binary since you mention they have the same underlying math)?

Hi Dax,

Right, simulating any oracle problem, like f(x) |x>, is equivalent to a 2^n * 2^n diagonal unitary matrix times a 2^n vector. In this point of view, yes we can use a diagonal gate in the Hidden Shift example. However, in this example, I think it is ok to leave it as is mainly because the oracle function consider in the example is simply

def make_oracle_f(qubits):
    """Implement function {f(x) = Σ_i x_(2i) x_(2i+1)}."""
    return [cirq.CZ(qubits[2 * i], qubits[2 * i + 1]) for i in range(len(qubits) // 2)]

Note CZ itself is already a diagonal gate. This is clean and good for example illustration. The benefit of using a diagonal gate will exhibit when we want to use other more complicated functions that we know f(x) but don't know how to write into existing primary gates easily. Similar opinion on Hamiltonian Binary. (I.e. if we know the oracle function boolean expression.)

Qiskit Diagonal gate has more functionalities (we have dense unitary and 1, 2-qubits decomposite representation only now). We can also consider making it more generalized first.