Uhrig Dynamical Control of a Three-Level System Via Non-Markovian Quantum State Diffusion

TL;DR

This paper demonstrates a method using non-Markovian quantum state diffusion to implement Uhrig dynamical decoupling on a three-level quantum system, effectively protecting it from noise in complex environments.

Contribution

It reformulates the non-Markovian QSD to include external control fields, enabling exact simulation and protection of quantum states against noise without Trotter approximations.

Findings

Protection of quantum states against colored noise.

Control efficacy depends on environment memory time.

Method applicable to systems with infinite environmental degrees of freedom.

Abstract

In this paper, we use the quantum state diffusion (QSD) equation to implement the Uhrig dynamical decoupling (UDD) to a three-level quantum system coupled to a non-Markovian reservoir comprising of infinite numbers of degrees of freedom. For this purpose, we first reformulate the non-Markovian QSD to incorporate the effect of the external control fields. With this stochastic QSD approach, we demonstrate that an unknown state of the three-level quantum system can be universally protected against both colored phase and amplitude noises when the control-pulse sequences and control operators are properly designed. The advantage of using non-Markovian quantum state diffusion equations is that the control dynamics of open quantum systems can be treated exactly without using Trotter product formula and be efficiently simulated even when the environment comprise of infinite numbers of degrees of freedom. We also show how the control efficacy depends on the environment memory time and the designed time points of applied control pulses.