Performance enhancements: observe_n and sample_n broadcast functions

[amccaskey]

#62

What's changing

• Use custatevecApplyPauliRotation for rx,ry,rz (faster than just custatevecApplyMatrix)
• CircuitSimulator batch mode (keep state memory alive during batch execution, faster than allocation, operation, deallocation over and over again)
• Simulators compute expectation value via in-memory matrix-vector product and dot product (<psi | H | psi>, faster for lower qubit counts than sampling the state).
• observe_n and sample_n batch mode execution (faster than iterating over many observe / sample calls)
• observe_n and sample_n distribute work to all available QPUs on the platform.

Runtime Improvements Example

For the following code,

n_samples = 5000
h = spin.z(0) 
times = []
for n_qubits in range(2, 16, 1): 
    n_parameters = n_qubits*3
    parameters = np.random.default_rng(13).uniform(low=0, high=1, size = (n_samples,n_parameters))
    np.random.seed(1)

    kernel, params = cudaq.make_kernel(list)
    qubits = kernel.qalloc(n_qubits)
    qubits_list = list(range(n_qubits))

    for i in range(n_qubits):
        kernel.rx(params[i], qubits[i])
    for i in range(n_qubits):
        kernel.ry(params[i + n_qubits], qubits[i])
    for i in range(n_qubits):
        kernel.rz(params[i + n_qubits*2], qubits[i])
    for q1, q2 in zip(qubits_list[0::2], qubits_list[1::2]):
        kernel.cz(qubits[q1], qubits[q2])

    t = []
    for _ in range(1): 
        start = timeit.default_timer()
        exp_vals = cudaq.observe_n(kernel, h, parameters)
        # old way, in main branch now
        # exp_vals = [cudaq.observe(kernel, h, parameters[i]).expectation_z() for i in range(parameters.shape[0])]
        end = timeit.default_timer()
        assert len(exp_vals) == n_samples
        t.append(end-start)
    
    times.append(statistics.mean(t))

we get the following runtime plots

[boschmitt]

Overall LGTM, thanks @amccaskey.

I would still want @anthony-santana, which has more familiarity with the python API, to look over.