Fidelity Between Unitary Operators and the Generation of Gates Robust Against Off-Resonance Perturbations

TL;DR

This paper develops a fidelity-based approach to design quantum gates that are robust against off-resonance errors, using functional expansion and multi-objective optimization to improve experimental feasibility.

Contribution

It introduces a novel fidelity expansion method for robust gate implementation and combines it with evolutionary optimization for practical control pulse design.

Findings

Fidelity expansion matches Magnus and Dyson first-order results

Optimized control pulses improve gate robustness

Multi-objective optimization balances robustness and feasibility

Abstract

We perform a functional expansion of the fidelity between two unitary matrices in order to find the necessary conditions for the robust implementation of a target gate. Comparison of these conditions with those obtained from the Magnus expansion and Dyson series shows that they are equivalent in first order. By exploiting techniques from robust design optimization, we account for issues of experimental feasibility by introducing an additional criterion to the search for control pulses. This search is accomplished by exploring the competition between the multiple objectives in the implementation of the NOT gate by means of evolutionary multi-objective optimization.