Memory-induced geometric phase in non-Markovian open systems

TL;DR

This paper investigates how non-Markovian environmental memory effects influence the geometric phase in open quantum systems, which is crucial for quantum computing accuracy.

Contribution

It introduces a microscopic model to analyze geometric phases in open systems, independent of master equations, highlighting the impact of non-Markovian environments.

Findings

Geometric phase can be obtained without master equations.

Non-Markovian environments significantly modify the geometric phase.

Environmental memory effects are fully incorporated into the model.

Abstract

Geometric phases have been shown to be feasible in implementing quantum gates to perform quantum information processing. For all the realistic applications, the environmental influence on the geometric phase and decoherence such as memory effects must be properly considered in order to achieve the required precision in geometric quantum computation. In this paper, we study the geometric phase for a generic open quantum system based on a microscopic model. A remarkable feature of the open system's geometric phase obtained from our theoretical formulation is that the geometric phase can be obtained regardless of the existence of the master equations, while the environmental noise features such as memory effects are fully accounted for. We demonstrate that the geometric phases for a general open quantum system can be fundamentally modified by its non-Markovian environments.