Augmented fidelities for single qubit gates

TL;DR

This paper introduces augmented fidelity measures for single and two-qubit gates that, by relaxing the uniform state distribution assumption, can better differentiate noise models like Pauli channels with different axis-specific noise rates.

Contribution

It analytically and numerically shows how modified fidelity measures can distinguish specific noise characteristics, extending the standard average gate fidelity approach.

Findings

Augmented fidelities differentiate noise models more effectively.

Analytical results for single-qubit cases.

Numerical simulations for two-qubit gates.

Abstract

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.