def main(nshots, backend):
'''Variationally find a maximally entangled state and the correct measurement angle
for violation of Bell inequalities.
Args:
nshots: number of shots to use for the minimization.
backend: choice of backend to run the example in.
'''
set_backend(backend)
initial_parameters = np.random.uniform(0, 2 * np.pi, 2)
circuits = set_parametrized_circuits()
best, params, _ = optimize(cost_function,
initial_parameters,
args=(circuits, nshots))
print(f'Cost: {best}\n')
print(f'Parameters: {params}\n')
print(f'Angles for the RY gates: {(params*180/np.pi)%360} in degrees.\n')
frequencies = []
for circuit in circuits:
circuit.set_parameters(params)
frequencies.append(circuit(nshots=nshots).frequencies())
chsh = compute_chsh(frequencies, nshots)
print(f'CHSH inequality value: {chsh}\n')
print(f'Target: {np.sqrt(2)*2}\n')
print(
f'Relative distance: {100*np.abs(np.abs(chsh)-np.sqrt(2)*2)/np.sqrt(2)*2}%\n'
)
def minimize(self, initial_parameters, method="BFGS", options=None,
messages=False):
"""Optimize the free parameters of the scheduling function.
Args:
initial_parameters (np.ndarray): Initial guess for the variational
parameters that are optimized.
The last element of the given array should correspond to the
guess for the total evolution time T.
method (str): The desired minimization method.
One of ``"cma"`` (genetic optimizer), ``"sgd"`` (gradient descent) or
any of the methods supported by
`scipy.optimize.minimize <https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html>`_.
options (dict): a dictionary with options for the different optimizers.
messages (bool): If ``True`` the loss evolution is shown during
optimization.
"""
self.opt_messages = messages
if method == "sgd":
loss = self._loss
else:
loss = lambda p, ae, h1, msg, hist: K.to_numpy(self._loss(p, ae, h1, msg, hist))
args = (self, self.hamiltonian.h1, self.opt_messages, self.opt_history)
result, parameters, extra = optimizers.optimize(
loss, initial_parameters, args=args, method=method, options=options)
if isinstance(parameters, K.tensor_types) and not len(parameters.shape): # pragma: no cover
# some optimizers like ``Powell`` return number instead of list
parameters = [parameters]
self.set_parameters(parameters)
return result, parameters, extra
def test_vqc(method, options, compile, filename):
"""Performs a VQE circuit minimization test."""
def myloss(parameters, circuit, target):
circuit.set_parameters(parameters)
state = circuit().tensor
return 1 - np.abs(np.dot(np.conj(target), state))
nqubits = 6
nlayers = 4
# Create variational circuit
c = models.Circuit(nqubits)
for l in range(nlayers):
c.add((gates.RY(q, theta=0) for q in range(nqubits)))
c.add((gates.CZ(q, q+1) for q in range(0, nqubits-1, 2)))
c.add((gates.RY(q, theta=0) for q in range(nqubits)))
c.add((gates.CZ(q, q+1) for q in range(1, nqubits-2, 2)))
c.add(gates.CZ(0, nqubits-1))
c.add((gates.RY(q, theta=0) for q in range(nqubits)))
# Optimize starting from a random guess for the variational parameters
np.random.seed(0)
x0 = np.random.uniform(0, 2*np.pi, 2*nqubits*nlayers + nqubits)
data = np.random.normal(0, 1, size=2**nqubits)
# perform optimization
best, params, _ = optimize(myloss, x0, args=(c, data), method=method,
options=options, compile=compile)
if filename is not None:
utils.assert_regression_fixture(params, filename)