Dynamical-Corrected Nonadiabatic Geometric Quantum Computation

TL;DR

This paper introduces a dynamical-corrected nonadiabatic geometric quantum computation scheme that enhances robustness against errors and decoherence, advancing towards fault-tolerant quantum computing with practical implementations.

Contribution

It develops a general dynamical correction method for nonadiabatic geometric gates, improving their error resilience and compatibility with various quantum systems.

Findings

Enhanced robustness of geometric gates against systematic errors.

Effective suppression of decoherence effects using DFS coding.

Potential for implementation in diverse quantum platforms.

Abstract

Recently, nonadiabatic geometric quantum computation has been received great attentions, due to its fast operation and intrinsic error resilience. However, compared with the corresponding dynamical gates, the robustness of implemented nonadiabatic geometric gates based on the conventional single-loop scheme still has the same order of magnitude due to the requirement of strict multi-segment geometric controls, and the inherent geometric fault-tolerance characteristic is not fully explored. Here, we present an effective geometric scheme combined with a general dynamical-corrected technique, with which the super-robust nonadiabatic geometric quantum gates can be constructed over the conventional single-loop and two-loop composite-pulse strategies, in terms of resisting the systematic error, i.e., $\sigma_x$ error. In addition, combined with the decoherence-free subspace (DFS) coding, the resulting geometric gates can also effectively suppress the $\sigma_z$ error caused by the collective dephasing. Notably, our protocol is a general one with simple experimental setups, which can be potentially implemented in different quantum systems, such as Rydberg atoms, trapped ions and superconducting qubits. These results indicate that our scheme represents a promising way to explore large-scale fault-tolerant quantum computation.