Department of Physics, University of Illinois at Urbana-Champaign, Illinois 61801, USA.
IQUIST and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Illinois 61801, USA.
Phys Rev Lett. 2022 Mar 4;128(9):090501. doi: 10.1103/PhysRevLett.128.090501.
The theory of open quantum systems lays the foundation for a substantial part of modern research in quantum science and engineering. Rooted in the dimensionality of their extended Hilbert spaces, the high computational complexity of simulating open quantum systems calls for the development of strategies to approximate their dynamics. In this Letter, we present an approach for tackling open quantum system dynamics. Using an exact probabilistic formulation of quantum physics based on positive operator-valued measure, we compactly represent quantum states with autoregressive neural networks; such networks bring significant algorithmic flexibility due to efficient exact sampling and tractable density. We further introduce the concept of string states to partially restore the symmetry of the autoregressive neural network and improve the description of local correlations. Efficient algorithms have been developed to simulate the dynamics of the Liouvillian superoperator using a forward-backward trapezoid method and find the steady state via a variational formulation. Our approach is benchmarked on prototypical one-dimensional and two-dimensional systems, finding results which closely track the exact solution and achieve higher accuracy than alternative approaches based on using Markov chain Monte Carlo method to sample restricted Boltzmann machines. Our Letter provides general methods for understanding quantum dynamics in various contexts, as well as techniques for solving high-dimensional probabilistic differential equations in classical setups.
开放量子系统理论为现代量子科学和工程的大部分研究奠定了基础。源于其扩展希尔伯特空间的维数，模拟开放量子系统的计算复杂性很高，需要开发策略来近似其动力学。在这封信中，我们提出了一种处理开放量子系统动力学的方法。我们使用基于正算子值测度的量子物理的精确概率公式，使用自回归神经网络紧凑地表示量子态；由于有效的精确采样和可处理的密度，这些网络具有显著的算法灵活性。我们进一步引入了字符串态的概念，以部分恢复自回归神经网络的对称性，并改善局部相关性的描述。我们已经开发了有效的算法来使用前向后梯形方法模拟李雅普诺夫超算符的动力学，并通过变分公式找到稳态。我们的方法在典型的一维和二维系统上进行了基准测试，结果与精确解紧密吻合，并比基于使用马尔可夫链蒙特卡罗方法对受限玻尔兹曼机进行采样的替代方法具有更高的准确性。我们的信提供了在各种情况下理解量子动力学的一般方法，以及在经典设置中解决高维概率微分方程的技术。
