cudaq.kernels supported by hardware-efficient ansatz

[Squirtle007]

Required prerequisites

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Describe the feature

A related issue was being tracked here #361.

Currently, cudaq.kernels does not support the hardware-efficient ansatz (HWE), which is valuable for variational quantum algorithms like VQE in reducing computation and simulation costs. Although HWE is included in this directory, it cannot be used.

To be precise,
cudaq.kernels.hwe is accessible, but subsequent cudaq.observe call will raise an error:
RuntimeError: hwe is not a valid kernel to call (cudaq.kernels).
and CUDA-Q built-in optimizers can not be used accordingly.

A simple modified version with JIT decorator (aligning to uccsd):

@cudaq.kernel
def hwe(qubits:cudaq.qview, numQubits:int, numLayers:int, parameters:list[float]):
    """
    Generate the hardware-efficient CUDA-Q kernel.

    Args:
        qubits (:class:`qview`): Pre-allocated qubits
        `numQubits` (int): Number of qubits
        `numLayers` (int): Number of layers
        parameters (List[float]): The list of parameters
    """

    cnotCoupling = [[int(i), int(i+1)] for i in range(numQubits - 1)]

    thetaCounter = 0
    for i in range(numQubits):
        ry(parameters[thetaCounter], qubits[i])
        rz(parameters[thetaCounter + 1], qubits[i])
        thetaCounter = thetaCounter + 2

    for i in range(numLayers):
        for cnot in cnotCoupling:
            cx(qubits[cnot[0]], qubits[cnot[1]])
        for q in range(numQubits):
            ry(parameters[thetaCounter], qubits[q])
            rz(parameters[thetaCounter + 1], qubits[q])
            thetaCounter += 2

[amccaskey]

This kernel is on the roadmap for CUDA-QX Solvers library cudaq_solvers.stateprep.hwe(...).

[Squirtle007]

That would be great, thanks so much.