# Composite nonadiabatic holonomic quantum computation

## TL;DR

This paper introduces a composite scheme for nonadiabatic holonomic quantum gates that reduces systematic control errors while maintaining robustness, especially effective for short evolution times and compatible with decoherence-free subspaces.

## Contribution

A novel composite approach to realize nonadiabatic holonomic gates that suppresses systematic errors without losing holonomic robustness.

## Key findings

- The scheme effectively suppresses systematic errors.
- It preserves holonomic robustness during short evolution periods.
- It can be integrated with decoherence-free subspaces for enhanced protection.

## Abstract

Nonadiabatic holonomic quantum computation has robust feature in suppressing control errors because of its holonomic feature. However, this kind of robust feature is challenged since the usual way of realizing nonadiabatic holonomic gates introduces errors due to systematic errors in the control parameters. To resolve this problem, we here propose a composite scheme to realize nonadiabatic holonomic gates. Our scheme can suppress systematic errors while preserving holonomic robustness. It is particularly useful when the evolution period is shorter than the coherence time. We further show that our composite scheme can be protected by decoherence-free subspaces. In this case, the strengthened robust feature of our composite gates and the coherence stabilization virtue of decoherence-free subspaces are combined.