Nonadiabatic Holonomic Quantum Computation via Path Optimization

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 sen-sitive 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 PON-HQC 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.

Automated summary

Nonadiabatic holonomic quantum computation (NHQC) is a geometric approach that uses fast evolution processes to overcome noise, but is sensitive to systematic noise and error. We propose a path-optimized NHQC scheme based on non-Abelian geometric phase, where a geometric gate can be constructed by different evolution paths, with each path responding differently to systematic noise. Numerical simulation shows that our optimized scheme outperforms conventional NHQC in terms of fidelity and robustness of gates. Additionally, we suggest implementing our strategy on superconducting quantum circuits.