Nonadiabatic Holonomic Quantum Computation via Path Optimization

Abstract

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