An average gate fidelity is a standard performance metric to quantify deviation between an ideal unitary gate transformation and its realistic experimental implementation. The average is taken with respect to states uniformly distributed over the full Hilbert space. We analytically (single-qubit) and numerically (two-qubit) show how this average changes if the uniform distribution condition is relaxed, replaced by parametrized distributions - polar cap and von Mises-Fisher distributions - and how the resulting fidelities can differentiate certain noise models. In particular, we demonstrate that Pauli channels with different noise rates along the three axes can be faithfully distinguished using these augmented fidelities.
@article{arxiv.2006.03086,
title = {Augmented fidelities for single qubit gates},
author = {Filip Wudarski and Jeffrey Marshall and Andre Petukhov and Eleanor Rieffel},
journal= {arXiv preprint arXiv:2006.03086},
year = {2020}
}