Error-Resilient Floquet Geometric Quantum Computation

TL;DR

This paper introduces Floquet geometric quantum computation (FGQC), a new error-resilient scheme using periodically driven systems, demonstrating high-fidelity gates and robustness against noise and control errors.

Contribution

The study proposes a novel Floquet GQC scheme based on a new non-Abelian geometric phase, with practical implementations and numerical validation showing high gate fidelity and robustness.

Findings

Gate fidelities approximately 0.9992 for Z and X gates.

FGQC gates are robust against global control errors.

Numerical simulations confirm high performance under noise and imperfections.

Abstract

We proposed a new geometric quantum computation (GQC) scheme, called Floquet GQC (FGQC), where error-resilient geometric gates based on periodically driven two-level systems can be constructed via a new non-Abelian geometric phase proposed in a recent study [V. Novi\^{c}enko \textit{et al}, Phys. Rev. A 100, 012127 (2019) ]. Based on Rydberg atoms, we gave possible implementations of universal single-qubit gates and a nontrivial two-qubit gate for FGQC. By using numerical simulation, we evaluated the performance of the FGQC Z and X gates in the presence of both decoherence and a certain kind of systematic control error. The gate fidelities of the Z and X gates are $F_{X,\text{gate}}\approx F_{Z,\text{gate}}\approx 0.9992$. The numerical results provide evidence that FGQC gates can achieve fairly high gate fidelities even in the presence of noise and control imperfection. In addition, we found FGQC is robust against global control error, both analytical demonstration and numerical evidence were given. Consequently, this study makes an important step towards robust geometric quantum computation.