Time optimal holonomic quantum computation

TL;DR

This paper explores the optimal conditions for implementing fast, high-fidelity holonomic quantum gates in a three-level system, balancing speed to reduce decoherence with the validity of the rotating wave approximation.

Contribution

It analyzes the trade-off between decoherence and RWA validity, identifying the optimal regime for holonomic quantum gate operation.

Findings

Optimal regime balances speed and RWA validity.

High-speed gates reduce decoherence effects.

Breakdown of RWA impacts gate dynamics.

Abstract

A three-level system can be used in a $\Lambda$-type configuration in order to construct a universal set of quantum gates through the use of non-Abelian non-adiabatic geometrical phases. Such construction allows for high-speed operation times which diminish the effects of decoherence. This might be, however, accompanied by a breakdown of the validity of the rotating wave approximation (RWA) due to the comparable time scale between counter-rotating terms and the pulse length, which greatly affects the dynamics. Here, we investigate the trade-off between dissipative effects and the RWA validity, obtaining the optimal regime for the operation of the holonomic quantum gates.