Nonadiabatic Holonomic Quantum Computation and Its Optimal Control

TL;DR

This paper reviews recent progress in nonadiabatic holonomic quantum computation, emphasizing optimal control methods to enhance gate fidelity and robustness, and discusses physical realizations and experimental demonstrations.

Contribution

It provides a comprehensive overview of optimal control strategies and experimental implementations for nonadiabatic holonomic quantum gates, highlighting their advantages over traditional methods.

Findings

Optimal control improves gate fidelity and robustness.

Holonomic gates can outperform dynamical gates under certain conditions.

Experimental realizations demonstrate practical feasibility.

Abstract

Geometric phase has the intrinsic property of being resistant to some types of local noises as it only depends on global properties of the evolution path. Meanwhile, the non-Abelian geometric phase is in the matrix form, and thus can naturally be used to implement high performance quantum gates, i.e., the so-called holonomic quantum computation. This article reviews recent advances in nonadiabatic holonomic quantum computation, and focuses on various optimal control approaches that can improve the gate performance, in terms of the gate fidelity and robustness. Besides, we also pay special attention to its possible physical realizations and some concrete examples of experimental realizations. Finally, with all these efforts, within state-of-the-art technology, the performance of the implemented holonomic quantum gates can outperform the conventional dynamical ones, under certain conditions.