近日，深圳大学物理与光电工程学院的李俊及其研究团队取得一项新进展。经过不懈努力，他们实现马尔可夫量子系统的鲁棒量子最优控制。相关研究成果已于2024年7月1日在国际知名学术期刊《物理评论A》上发表。

本文提出了一种鲁棒量子最优控制方法来处理马尔可夫噪声。其基本思想是，将马尔可夫噪声信道视为扰动，通过扰动展开项定量表征噪声引起的误差演化，并将其作为待抑制的目标函数。在优化过程中，通过使控制目标函数最大化，同时使马尔可夫噪声引起的扰动项逐级最小化来获得最优控制。作为示例，研究人员首先将该方法应用于两层和三层Λ系统上的量子态转移任务，然后用它来设计两层和三层阶梯系统中的量子门，都是在马尔可夫噪声下。

仿真结果表明，该方法可以显著提高量子态转移保真度，而对门保真度的改善非常有限。本文提出的方法是通用的，可以扩展到提高多电平或多量子比特量子系统在马尔可夫噪声下的各种控制任务的性能。

据悉，抵抗各种噪声效应是精确操纵量子系统的关键。对于静态或缓慢变化的噪声，人们开发了许多有效的降噪策略，如复合脉冲和动态解耦。然而，对于马尔可夫极限下的快速波动噪声，相干量子控制是否以及在多大程度上可以增强量子工程任务仍然不清楚，并且探索较少。

附：英文原文

Title: Robust quantum optimal control for Markovian quantum systems

Author: Ran Liu, Xiaodong Yang, Jun Li

Issue&Volume: 2024/07/01

Abstract: Resisting diverse noise effects is crucial for the accurate manipulation of quantum systems. For static or slowly varying noises, many efficient noise mitigation strategies have been developed, such as composite pulses and dynamical decoupling. However, for fast fluctuating noise in the Markovian limit, whether and to what extent coherent quantum control can enhance quantum engineering tasks remains unclear and less explored. Here, we propose a robust quantum optimal control method to tackle Markovian noises. The basic idea is that, regarding the Markovian noise channel as perturbation, we quantitatively characterize the noise-induced error evolution by the perturbative expansion term, and then take them as the objective functions to be suppressed. During optimization, the optimal controls are obtained by maximizing the control target function and meanwhile minimizing the perturbative terms due to Markovian noise order by order. As demonstration examples, we first apply our method to quantum state transfer tasks on two-level and three-level Λ systems, then use it to design quantum gates in two-level and three-level ladder systems, all under Markovian noises. The simulation results illustrate that our method can notably enhance quantum state transfer fidelities and have very limited improvement on gate fidelities. The method presented here is versatile and can be extended to enhance the performance of various control tasks under Markovian noise in multilevel or multiqubit quantum systems.

DOI: 10.1103/PhysRevA.110.012402

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.012402