Nonadiabatic Holonomic Quantum Computation via Path Optimization

TL;DR

This paper introduces a path-optimized nonadiabatic holonomic quantum computation scheme that enhances gate fidelity and robustness by selecting evolution paths less sensitive to systematic noise, demonstrated via numerical simulations and feasible for superconducting circuits.

Contribution

It proposes a novel path optimization method for NHQC that improves gate performance and robustness against systematic errors, with practical implementation strategies.

Findings

Optimized paths significantly increase gate fidelity.

The scheme outperforms conventional NHQC in robustness.

Feasible implementation in superconducting circuits is demonstrated.

Abstract

Nonadiabatic holonomic quantum computation (NHQC) is implemented by fast evolution processes in a geometric way to withstand local noises. However, recent works of implementing NHQC are sensitive to the systematic noise and error. Here, we present a path-optimized NHQC (PONHQC) scheme based on the non-Abelian geometric phase, and find that a geometric gate can be constructed by different evolution paths, which have different responses to systematic noises. Due to the flexibility of the PONHQC scheme, we can choose an optimized path that can lead to excellent gate performance. Numerical simulation shows that our optimized scheme can greatly outperform the conventional NHQC scheme, in terms of both fidelity and robustness of the gates. In addition, we propose to implement our strategy on superconducting quantum circuits with decoherence-free subspace encoding with the experiment-friendly two-body exchange interaction. Therefore, we present a flexible NHQC scheme that is promising for the future robust quantum computation.