Hartmann Michael J, Carleo Giuseppe
Institute of Photonics and Quantum Sciences, Heriot-Watt University Edinburgh EH14 4AS, United Kingdom.
Google Research, Erika-Mann-Str. 33, 80636 München, Germany.
Phys Rev Lett. 2019 Jun 28;122(25):250502. doi: 10.1103/PhysRevLett.122.250502.
In experimentally realistic situations, quantum systems are never perfectly isolated and the coupling to their environment needs to be taken into account. Often, the effect of the environment can be well approximated by a Markovian master equation. However, solving this master equation for quantum many-body systems becomes exceedingly hard due to the high dimension of the Hilbert space. Here we present an approach to the effective simulation of the dynamics of open quantum many-body systems based on machine-learning techniques. We represent the mixed many-body quantum states with neural networks in the form of restricted Boltzmann machines and derive a variational Monte Carlo algorithm for their time evolution and stationary states. We document the accuracy of the approach with numerical examples for a dissipative spin lattice system.
在实验现实的情况下，量子系统永远不会被完美隔离，需要考虑其与环境的耦合。通常，环境的影响可以通过马尔可夫主方程得到很好的近似。然而，由于希尔伯特空间的高维度，求解这个量子多体系统的主方程变得极其困难。在此，我们提出一种基于机器学习技术对开放量子多体系统动力学进行有效模拟的方法。我们用受限玻尔兹曼机形式的神经网络来表示混合多体量子态，并推导出一种用于其时间演化和稳态的变分蒙特卡罗算法。我们用一个耗散自旋晶格系统的数值例子证明了该方法的准确性。
