# Environment-assisted holonomic quantum maps

## TL;DR

This paper demonstrates that structured environments can enhance the robustness of nonadiabatic holonomic quantum gates against systematic errors by maintaining geometric properties, as shown in a spin-bath model.

## Contribution

It introduces an environment-assisted approach to extend the error resilience of holonomic quantum gates while preserving their geometric nature.

## Key findings

- Environment interaction can reduce systematic error sensitivity.
- The scheme maintains geometric properties of quantum evolution.
- Proof-of-concept shown in a spin-bath model.

## Abstract

Holonomic quantum computation uses non-Abelian geometric phases to realize error resilient quantum gates. Nonadiabatic holonomic gates are particularly suitable to avoid unwanted decoherence effects, as they can be performed at high speed. By letting the computational system interact with a structured environment, we show that the scope of error resilience of nonadiabatic holonomic gates can be widened to include systematic parameter errors. Our scheme maintains the geometric properties of the evolution and results in an environment-assisted holonomic quantum map that can mimic the effect of a holonomic gate. We demonstrate that the sensitivity to systematic errors can be reduced in a proof-of-concept spin-bath model.