# Geometric phase gates in dissipative quantum dynamics

## TL;DR

This paper analyzes how environmental noise affects geometric phase gates in trapped ions and proposes a method to counteract dissipation effects, improving gate fidelity and robustness at both zero and finite temperatures.

## Contribution

It introduces a strategy to compensate for dissipative effects in geometric phase gates, enhancing their performance in realistic noisy environments.

## Key findings

- Dissipative effects induce additional phases and coherence loss.
- The proposed compensation strategy restores the ideal phase and motional state.
- The method improves gate fidelity and robustness against errors.

## Abstract

Trapped ions are among the most promising candidates for performing quantum information processing tasks. Recently, it was demonstrated how the properties of geometric phases can be used to implement an entangling two qubit phase gate with significantly reduced operation time while having a built-in resistance against certain types of errors (Palmero et. al., Phys. Rev. A 95, 022328 (2017)). In this article, we investigate the influence of both quantum and thermal fluctuations on the geometric phase in the Markov regime. We show that additional environmentally induced phases as well as a loss of coherence result from the non-unitary evolution, even at zero temperature. We connect these effects to the associated dynamical and geometrical phases. This suggests a strategy to compensate the detrimental environmental influences and restore some of the properties of the ideal implementation. Our main result is a strategy for zero temperature to construct forces for the geometric phase gate which compensate the dissipative effects and leave the produced phase as well as the final motional state identical to the isolated case. We show that the same strategy helps also at finite temperatures. Furthermore, we examine the effects of dissipation on the fidelity and the robustness of a two qubit phase gate against certain error types.