def cost(weights, phi, gamma, J, W, epsilon=1e-10):
return np.trace(
W
@ np.linalg.inv(
J.T @ CFIM(weights, phi, gamma) @ J + np.eye(2) * epsilon
)
)
def shadow_bound(error, observables, failure_rate=0.01):
"""
Calculate the shadow bound for the Pauli measurement scheme.
Implements Eq. (S13) from https://arxiv.org/pdf/2002.08953.pdf
Args:
error (float): The error on the estimator.
observables (list) : List of matrices corresponding to the observables we intend to
measure.
failure_rate (float): Rate of failure for the bound to hold.
Returns:
An integer that gives the number of samples required to satisfy the shadow bound and
the chunk size required attaining the specified failure rate.
"""
M = len(observables)
K = 2 * np.log(2 * M / failure_rate)
shadow_norm = (
lambda op: np.linalg.norm(
op - np.trace(op) / 2 ** int(np.log2(op.shape[0])), ord=np.inf
)
** 2
)
N = 34 * max(shadow_norm(o) for o in observables) / error ** 2
return int(np.ceil(N * K)), int(K)
def operator_2_norm(R):
"""
Calculate the operator 2-norm.
Args:
R (array): The operator whose norm we want to calculate.
Returns:
Scalar corresponding to the norm.
"""
return np.sqrt(np.trace(R.conjugate().transpose() @ R))
def TraceDistance(A, B):
return 0.5 * np.trace(np.absolute(np.add(A, -1*B)))
def cost(self, weights, inputs_1=None, inputs_2=None):
ensemble_1 = self.embedding.generate_ensemble(inputs_1, weights)
ensemble_2 = self.embedding.generate_ensemble(inputs_2, weights)
observable = self.class_priors[0] * ensemble_1 - self.class_priors[
1] * ensemble_2
return 1 - np.real(np.trace(observable @ observable))