Simulates HHL with matrix input, and outputs Pauli observables of the
    resulting qubit state |x>.
    Expected observables are calculated from the expected solution |x>.

def main():
    """
    Simulates HHL with matrix input, and outputs Pauli observables of the
    resulting qubit state |x>.
    Expected observables are calculated from the expected solution |x>.
    """

    # Eigendecomposition:
    #   (4.537, [-0.971555, -0.0578339+0.229643j])
    #   (0.349, [-0.236813, 0.237270-0.942137j])
    # |b> = (0.64510-0.47848j, 0.35490-0.47848j)
    # |x> = (-0.0662724-0.214548j, 0.784392-0.578192j)
    A = np.array([[4.30213466-6.01593490e-08j,
                   0.23531802+9.34386156e-01j],
                  [0.23531882-9.34388383e-01j,
                   0.58386534+6.01593489e-08j]])
    t = 0.358166*math.pi
    register_size = 4
    input_prep_gates = [cirq.Rx(1.276359), cirq.Rz(1.276359)]
    expected = (0.144130, 0.413217, -0.899154)

    # Set C to be the smallest eigenvalue that can be represented by the
    # circuit.
    C = 2*math.pi / (2**register_size * t)

    # Simulate circuit
    print("Expected observable outputs:")
    print("X =", expected[0])
    print("Y =", expected[1])
    print("Z =", expected[2])
    print("Actual: ")
    simulate(hhl_circuit(A, C, t, register_size, *input_prep_gates))