Decoherence of quantum gates based on Aharonov-Anandan phases in a multistep scheme

TL;DR

This paper investigates how quantum decoherence affects Aharonov-Anandan geometric phase gates in a multistep scheme, comparing their robustness to dynamical gates and exploring factors that enhance fidelity and entanglement protection.

Contribution

It introduces a detailed analysis of decoherence effects on AA phase gates and identifies conditions that improve their robustness against environmental noise.

Findings

Fidelities of AA phase gates are enhanced by superpositions of environmental eigenstates.

Entanglement protection is improved by noncommutativity between qubit interaction and environmental coupling.

AA phase gates show different decoherence characteristics compared to dynamical phase gates.

Abstract

We study quantum decoherence of single-qubit and two-qubit Aharonov-Anandan (AA) geometric phase gates realized in a multistep scheme. Each AA gate is also compared with the dynamical phase gate performing the same unitary transformation within the same time period and coupled with the same environment, which is modeled as harmonic oscillators. It is found that the fidelities and the entanglement protection of the AA phase gates are enhanced by the states being superpositions of different eigenstates of the environmental coupling, and the noncommutativity between the qubit interaction and the environmental coupling.