Improving quantum gate performance through neighboring optimal control

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, although ${P}_{a}\ensuremath{\sim}{10}^{\ensuremath{-}4}$ 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 nonadiabatic rapid passage that has appeared in the literature. Performance improvements are substantial, both for ideal and nonideal controls. Under suitable conditions detailed in this paper, all gate error probabilities fall well below the target threshold of ${10}^{\ensuremath{-}4}$.