Evaluation metrics

Different metrics used for evaluation.

Base norm

---

source

BaseNorm

def BaseNorm(
    args:VAR_POSITIONAL, kwargs:VAR_KEYWORD
):

Base class for norms.

Unitary distances

---

source

UnitaryFrobeniusNorm

def UnitaryFrobeniusNorm(
    args:VAR_POSITIONAL, kwargs:VAR_KEYWORD
):

The Frobenius-Norm for unitaries: defined in https://arxiv.org/pdf/2106.05649.pdf.

---

source

UnitaryInfidelityNorm

def UnitaryInfidelityNorm(
    args:VAR_POSITIONAL, kwargs:VAR_KEYWORD
):

The Infidelity-Norm for unitaries: defined in https://link.aps.org/accepted/10.1103/PhysRevA.95.042318, TABLE I: 1.

Test the metrics on random unitaries:

approx_U = torch.tensor(unitary_group.rvs(8))
target_U = torch.tensor(unitary_group.rvs(8))

print(UnitaryFrobeniusNorm.name())
UnitaryFrobeniusNorm.distance(target_U, target_U), UnitaryFrobeniusNorm.distance(approx_U, target_U)

Frobenius-Norm

(tensor(0., dtype=torch.float64), tensor(8.5523, dtype=torch.float64))

print(UnitaryInfidelityNorm.name())
UnitaryInfidelityNorm.distance(target_U, target_U), UnitaryInfidelityNorm.distance(approx_U, target_U)

Unitary-Infidelity

(tensor(4.4409e-16, dtype=torch.float64), tensor(0.9895, dtype=torch.float64))