Non-adiabatic Holonomic Gates realized by a single-shot implementation

TL;DR

This paper introduces a novel single-shot method for implementing arbitrary non-adiabatic holonomic one-qubit gates, enhancing efficiency and robustness in quantum computation by avoiding sequential gate operations.

Contribution

The paper presents a new scheme enabling direct realization of any single-qubit holonomic gate in a single step, using a three-level system driven by laser pulses, which was not previously achievable.

Findings

Single-shot implementation of arbitrary holonomic one-qubit gates achieved.

Scheme is compatible with existing non-adiabatic two-qubit gates.

Analysis of realistic error effects on the scheme.

Abstract

Non-adiabatic holonomic quantum computation has received increasing attention due to its robustness against control errors. However, all the previous schemes have to use at least two sequentially implemented gates to realize a general one-qubit gate. In this paper, we put forward a novelty scheme by which one can directly realize an arbitrary holonomic one-qubit gate with a single-shot implementation, avoiding the extra work of combining two gates into one. Based on a three-level model driven by laser pulses, we show that any single-qubit holonomic gate can be realized by varying the detuning, amplitude, and phase of lasers. Our scheme is compatible with previously proposed non-adiabatic holonomic two-qubit gates, combining with which the arbitrary holonomic one-qubit gates can play universal non-adiabatic holonomic quantum computation. We also investigate the effects of some unavoidable realistic errors on our scheme.