近日，奥地利因斯布鲁克大学的Tatiana Vovk与Hannes Pichler合作并取得一项新进展。经过不懈努力，他们对各种马尔可夫动力学解的量子轨迹纠缠进行研究。相关研究成果已于2024年7月8日在国际知名学术期刊《物理评论A》上发表。

在本文中，该研究团队研究了求解描述开放量子系统动力学主方程的，随机量子轨迹方法中的纠缠。首先，研究人员引入并比较了主方程的自适应轨迹展开。具体而言，该研究是在《Phys. Rev. Lett. 128, 243601 (2022)》的坚实基础上进一步展开的。研究人员首先聚焦于探索多种贪婪算法，旨在构建出具有极低平均纠缠熵的量子轨迹。

随后，他们深入分析了一维开放随机布朗电路中的多种典型展开方式，并成功界定了从面积定律到体积定律下纠缠轨迹转变的关键点。第三，他们比较了使用矩阵乘积状态的各种轨迹展开，与使用矩阵乘积算子的主方程的直接积分。通过具体动力学案例的展示，他们发现，在模拟成本上，随机轨迹的方法相较于矩阵乘积算子具有显著的指数级优势

据悉，经典量子多体动力学模拟的成本通常由系统中的纠缠量决定。

附：英文原文

Title: Quantum trajectory entanglement in various unravelings of Markovian dynamics

Author: Tatiana Vovk, Hannes Pichler

Issue&Volume: 2024/07/08

Abstract: The cost of classical simulations of quantum many-body dynamics is often determined by the amount of entanglement in the system. In this paper, we study entanglement in stochastic quantum trajectory approaches that solve master equations describing open quantum system dynamics. First, we introduce and compare adaptive trajectory unravelings of master equations. Specifically, building on [Phys. Rev. Lett. 128, 243601 (2022)], we study several greedy algorithms that generate trajectories with a low average entanglement entropy. Second, we consider various conventional unravelings of a one-dimensional open random Brownian circuit and locate the transition points from area- to volume-law-entangled trajectories. Third, we compare various trajectory unravelings using matrix product states with a direct integration of the master equation using matrix product operators. We provide concrete examples of dynamics, for which the simulation cost of stochastic trajectories is exponentially smaller than the one of matrix product operators.

DOI: 10.1103/PhysRevA.110.012207

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.012207