Recent Advances on Nonadiabatic Geometric Quantum Computation

TL;DR

This paper reviews recent progress in nonadiabatic geometric quantum computation, emphasizing theoretical frameworks, design principles, and numerical comparisons to improve gate fidelity and robustness in quantum computing.

Contribution

It provides a unified theoretical framework for nonadiabatic GQC, analyzes design principles with optimal control, and offers comprehensive numerical comparisons of protocols.

Findings

Nonadiabatic GQC approaches can be unified under a common framework.

Optimal control enhances the accuracy and noise resistance of geometric gates.

Numerical comparisons reveal practical limitations and performance differences among protocols.

Abstract

The geometric phase stands as a foundational concept in quantum physics, revealing deep connections between geometric structures and quantum dynamical evolution. Unlike dynamical phases, geometric phases exhibit intrinsic resilience to certain types of perturbation, making them particularly valuable for quantum information processing, where maintaining coherent quantum operations is essential. This article provides a review of geometric phases in the context of universal quantum gate construction, i.e., the geometric quantum computation (GQC), with special attention to recent progress in nonadiabatic implementations that enhance gate fidelity and/or operational robustness. We first review a unified theoretical framework that can encompass all existing nonadiabatic GQC approaches, then systematically examine the design principles of nonadiabatic geometric gates with a particular focus on how optimal control techniques can be leveraged to improve the accuracy and noise resistance. In addition, we conducted detailed numerical comparisons of various nonadiabatic GQC protocols, offering a quantitative assessment of their respective performance characteristics and practical limitations. Through this focused investigation, our aim is to provide researchers with both fundamental insights and practical guidance for advancing geometric approaches in quantum computing.