def U_c():
"""Unitary matrix rotating the ground state of the ancillary qubits
to |sqrt(c)> = U_c |0>."""
# Circuit mapping |00> to sqrt_c[0] |00> + sqrt_c[1] |01> + sqrt_c[2] |10>
qml.RY(-2 * np.arccos(sqrt_c[0]), wires=ancilla_idx)
qml.CRY(-2 * np.arctan(sqrt_c[2] / sqrt_c[1]),
wires=[ancilla_idx, ancilla_idx + 1])
qml.CNOT(wires=[ancilla_idx + 1, ancilla_idx])
def QNNLayer(self, params):
'''
Definition of a single ST step for
layering QNN
'''
ExcInts = params[0:3]
ExtField = params[3:6]
# Parameters for external
# field evol
Hx = ExtField[0]
Hy = ExtField[1]
Hz = ExtField[2]
H = np.sqrt(Hx**2 + Hy**2 + Hz**2)
# Parameter values for Qiskit
PHI = np.arctan2(Hy, Hx) + 2*np.pi
THETA = np.arccos(Hz/H)
LAMBDA = np.pi
# Cascade Spin pair interaction
for idx in range(self.num_spins-1):
# Convert to computational basis
qml.CNOT(wires=[idx, idx+1])
qml.Hadamard(wires=idx)
# Compute J3 phase
qml.RZ(ExcInts[2], wires=idx+1)
# Compute J1 phase
qml.RZ(ExcInts[0], wires=idx)
# Compute J2 Phase
qml.CNOT(wires=[idx, idx+1])
qml.RZ(-ExcInts[1], wires=idx+1)
qml.CNOT(wires=[idx, idx+1])
# Return to computational basis
qml.Hadamard(wires=idx)
qml.CNOT(wires=[idx, idx+1])
# Include external field
qml.U3(-THETA, -LAMBDA, -PHI, wires=idx)
qml.RZ(H, wires=idx)
qml.U3(THETA, PHI, LAMBDA, wires=idx)
# Include external field for last spin
qml.U3(-THETA, -LAMBDA, -PHI, wires=self.num_spins-1)
qml.RZ(H, wires=self.num_spins-1)
qml.U3(THETA, PHI, LAMBDA, wires=self.num_spins-1)
def compute_K(generator):
"""Compute the K hyperparameter controlling # iterations of amplification.
Args:
generator: An initialized circuit generator (one of the ones above)
"""
np.random.seed(0)
N = 50
target_prob_list = [
generator.target_prob([
np.random.uniform(low=0, high=2 * np.pi)
for j in range(generator.num_qubits)
]) for _ in range(N)
]
cosphi_list = [2 * p - 1 for p in target_prob_list]
cosPhi, cosPhi_error = np.mean(
cosphi_list), np.std(cosphi_list) / np.sqrt(N)
Phi = np.arccos(cosPhi)
K = int(np.pi / (2 * (np.pi - Phi)))
return K
def U_c_dagger():
"""Adjoint of U_c."""
qml.CNOT(wires=[ancilla_idx + 1, ancilla_idx])
qml.CRY(2 * np.arctan(sqrt_c[2] / sqrt_c[1]),
wires=[ancilla_idx, ancilla_idx + 1])
qml.RY(2 * np.arccos(sqrt_c[0]), wires=ancilla_idx)