Support for U3 gate

[anthony-santana]

Description

This PR completes the support for the changes added #1504 for all backends.

• Writes a decomposition pattern for the u3 gate in terms of rx and rz gates
• Adds a decomposition test to Quake tests
• Connects this decomposition pattern to all of the hardware backend configs
• Tests on each backend in C++ and Python if the u3 gate and its controlled variant is properly lowered and executed

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[anthony-santana]

The following code was used to benchmark the simulated accuracy of various decomposition patterns of the u3 gate.

The procedure is as follows.

For each simulator, at various different theta, phi, and lambda angles:

1. Run each kernel and get their respective measurement distributions.
2. Take the distance of each distribution from the desired distribution generated by the u3 gate — use the Wasserstein metric. Call this the “infidelity”
3. Keep a running sum of the infidelity for each kernel, and at the end, take the kernel that has the lowest total infidelity value

Results show that the qiskit and pennylane decompositions produce nearly identical results -- both of which are slightly off from the u3 gate.

import cudaq
import numpy as np
from scipy.stats import wasserstein_distance


@cudaq.kernel
def kernel(theta: float, phi: float, lam: float):
    q = cudaq.qubit()
    u3(theta, phi, lam, q)


@cudaq.kernel
def kernel_b(theta: float, phi: float, lam: float):
    """Trial decomposition."""
    q = cudaq.qubit()
    rx(theta, q)
    ry(phi, q)
    rz(lam, q)

@cudaq.kernel
def kernel_c(theta: float, phi: float, lam: float):
    """First decomposition pattern."""
    q = cudaq.qubit()
    rz(lam, q)
    rx(np.pi / 2, q)
    rz(theta, q)
    rx(-np.pi / 2, q)
    rz(phi, q)


@cudaq.kernel
def kernel_d(theta: float, phi: float, lam: float):
    """Second decomposition pattern"""
    q = cudaq.qubit()
    r1(phi+lam, q)
    rz (-1.*lam, q)
    ry (theta, q)
    rz (lam, q)


def convert_dict_to_distribution(result):
    distribution = None
    # This only works because we'll only be working with
    # single qubit results -- e.g, length 1 bit values instead
    # of bitstrings.
    for bit_value, count in result.items():
        if distribution is None:
            distribution = np.repeat(bit_value, repeats=count)
        else:
            distribution = np.append(distribution,
                                     np.repeat(bit_value, repeats=count))
    return distribution


iteration_count = 12
thetas = np.arange(0.0, 2 * np.pi, step=np.pi / iteration_count, dtype=float)
phis = np.arange(0.0, 2 * np.pi, step=np.pi / iteration_count, dtype=float)
lams = np.arange(0.0, 2 * np.pi, step=np.pi / iteration_count, dtype=float)

np.random.shuffle(thetas)
np.random.shuffle(phis)
np.random.shuffle(lams)

distribution_infidelity_b = 0.0
distribution_infidelity_c = 0.0
distribution_infidelity_d = 0.0

targets = [
    "tensornet", "tensornet-mps", "nvidia-mqpu-fp64", "density-matrix-cpu",
    "nvidia", "nvidia-fp64", "nvidia-mqpu", "nvidia-mqpu-mps" , "qpp-cpu" 
]
for target in targets:
    cudaq.set_target(target)
    for theta, phi, lam in zip(thetas, phis, lams):

        result = cudaq.sample(kernel, theta, phi, lam, shots_count=2000)
        distribution = convert_dict_to_distribution(result)
        # print("result = ", result)
        result_b = cudaq.sample(kernel_b, theta, phi, lam, shots_count=2000)
        distribution_b = convert_dict_to_distribution(result_b)
        # print("result_b = ", result_b)
        result_c = cudaq.sample(kernel_c, theta, phi, lam, shots_count=2000)
        distribution_c = convert_dict_to_distribution(result_c)
        # print("result_c = ", result_c)
        result_d = cudaq.sample(kernel_d, theta, phi, lam, shots_count=2000)
        distribution_d = convert_dict_to_distribution(result_d)
        # print("result_d = ", result_d)

        # print("distribution vs. itself = ", wasserstein_distance(distribution, distribution))
        # print("distribution b = ", wasserstein_distance(distribution, distribution_b))
        # print("distribution c = ", wasserstein_distance(distribution, distribution_c))
        # print("distribution d = ", wasserstein_distance(distribution, distribution_d))

        distribution_infidelity_b += wasserstein_distance(distribution,
                                                        distribution_b)
        distribution_infidelity_c += wasserstein_distance(distribution,
                                                        distribution_c)
        distribution_infidelity_d += wasserstein_distance(distribution,
                                                        distribution_d)

print("total infidelity, b = ", distribution_fidelity_b)
print("total infidelity, c = ", distribution_fidelity_c)
print("total infidelity, d = ", distribution_fidelity_d)

[anthony-santana]

/ok to test

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[github-actions]

CUDA Quantum Docs Bot: A preview of the documentation can be found here.

[anthony-santana]

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[github-actions]

CUDA Quantum Docs Bot: A preview of the documentation can be found here.

[anthony-santana]

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[khalatepradnya]

You may want to change this Python test - https://github.com/NVIDIA/cuda-quantum/blob/main/python/tests/backends/test_Quantinuum_LocalEmulation_kernel.py#L120. It should no longer raise error.

[anthony-santana]

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[github-actions]

CUDA Quantum Docs Bot: A preview of the documentation can be found here.

[khalatepradnya]

Changes looking good... I see CI needs to be addressed.
You can also remove this note from documentation - https://github.com/NVIDIA/cuda-quantum/blob/main/docs/sphinx/api/default_ops.rst?plain=1#L356

[anthony-santana]

/ok to test

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[anthony-santana]

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[github-actions]

CUDA Quantum Docs Bot: A preview of the documentation can be found here.

[anthony-santana]

/ok to test

Command Bot: Processing...

[github-actions]

CUDA Quantum Docs Bot: A preview of the documentation can be found here.