# Single-shot realization of nonadiabatic holonomic quantum gates in decoherence-free subspaces

## TL;DR

This paper introduces a single-shot protocol for nonadiabatic holonomic quantum gates in decoherence-free subspaces, reducing error exposure and resource use compared to previous multi-gate schemes.

## Contribution

It presents a novel single-shot method for implementing arbitrary one-qubit gates in decoherence-free subspaces, improving efficiency and robustness.

## Key findings

- Achieves arbitrary one-qubit gates with a single shot
- Reduces gate exposure time to errors
- Maintains robustness of holonomic and decoherence-free approaches

## Abstract

Nonadiabatic holonomic quantum computation in decoherence-free subspaces has attracted increasing attention recently, as it allows for high-speed implementation and combines both the robustness of holonomic gates and the coherence stabilization of decoherence-free subspaces. Since the first protocol of nonadiabatic holonomic quantum computation in decoherence-free subspaces, a number of schemes for its physical implementation have been put forward. However, all previous schemes require two noncommuting gates to realize an arbitrary one-qubit gate, which doubles the exposure time of gates to error sources as well as the resource expenditure. In this paper, we propose an alternative protocol for nonadiabatic holonomic quantum computation in decoherence-free subspaces, in which an arbitrary one-qubit gate in decoherence-free subspaces is realized by a single-shot implementation. The present protocol not only maintains the merits of the original protocol, but also avoids the extra work of combining two gates to implement an arbitrary one-qubit gate and thereby reduces the exposure time to various error sources.