Improving quantum gate performance through neighboring optimal control

TL;DR

This paper introduces a neighboring optimal control framework to enhance quantum gate performance, achieving error probabilities below the critical threshold for fault-tolerant quantum computing, demonstrated on gates from non-adiabatic rapid passage.

Contribution

The paper presents a novel neighboring optimal control method to improve quantum gate fidelity, applicable to existing gates, ensuring error rates meet fault-tolerance thresholds.

Findings

Gate error probabilities fall below 10^{-4}

Performance improvements are substantial for ideal controls

Applicable to gates from non-adiabatic rapid passage

Abstract

Successful implementation of a fault-tolerant quantum computation on a system of qubits places severe demands on the hardware used to control the many-qubit state. It is known that an accuracy threshold $P_{a}$ exists for any quantum gate that is to be used in such a computation. Specifically, the error probability $P_{e}$ for such a gate must fall below the accuracy threshold: $P_{e} < P_{a}$. Estimates of $P_{a}$ vary widely, though $P_{a}\sim 10^{-4}$ has emerged as a challenging target for hardware designers. In this paper we present a theoretical framework based on neighboring optimal control that takes as input a good quantum gate and returns a new gate with better performance. We illustrate this approach by applying it to all gates in a universal set of quantum gates produced using non-adiabatic rapid passage that has appeared in the literature. Performance improvements are substantial, both for ideal and non-ideal controls. Under suitable conditions detailed below, all gate error probabilities fall well below the target threshold of $10^{-4}$.