Variational Autoencoder Reconstruction of Complex Many-Body Physics
Variational Autoencoder Reconstruction of Complex Many-Body Physics
复制标题
DOI：
10.3390/e21111091
复制
发表时间：
2019-11-07
期刊：
影响因子：
2.7
通讯作者：
Ouerdane H
中科院分区：
文献类型：
--
作者：
Luchnikov IA;Ryzhov A;Stas PJ;Filippov SN;Ouerdane H
热力学是一门原理理论，它允许对各种复杂系统的宏观性质进行基本描述，从传统的系统，如结晶固体、气体、液体和热机，到更复杂的系统，如生物有机体和黑洞等等。感兴趣的物理量或平衡状态变量在状态方程中连接在一起，以提供有关所研究系统的信息，包括相变，因为以功和热的形式的能量和/或物质与其环境交换，从而产生熵。更准确的描述需要不同的框架，即统计力学和量子物理，以深入探索物理系统的微观属性，并将它们与其宏观属性联系起来。这些框架还允许超越均衡情况。考虑到研究现实系统的数学模型的复杂性显著增加，以及它们与环境的耦合限制了它们的动力学，建立在这些模型上的分析方法和数值方法在范围或适用性方面都显示出局限性。另一方面，机器学习，即数据驱动的方法，被证明对复杂量子系统的研究越来越有效。尤其是深度神经网络，已经成功地应用于多体量子动力学模拟和量子物质相表征。在这项工作中，我们展示了如何使用变分自动编码器(VAE)--深度学习领域中最先进的工具来模拟复杂系统的概率分布。更准确地说，我们利用信息完全正算符值度量将多体重构的量子力学问题转化为适合于VAE的统计问题。利用横向磁场中的典型量子伊辛模型，我们证明了对于哈密顿量的不同参数，即使系统经历了量子相变，也可以通过对层析数据的VAE学习来重建一整类量子多体系统的基态物理，例如，磁化强度和其他可观测的平均值。我们还讨论了与我们的方法相关的挑战，因为熵计算带来了特别的困难。
Thermodynamics is a theory of principles that permits a basic description of the macroscopic properties of a rich variety of complex systems from traditional ones, such as crystalline solids, gases, liquids, and thermal machines, to more intricate systems such as living organisms and black holes to name a few. Physical quantities of interest, or equilibrium state variables, are linked together in equations of state to give information on the studied system, including phase transitions, as energy in the forms of work and heat, and/or matter are exchanged with its environment, thus generating entropy. A more accurate description requires different frameworks, namely, statistical mechanics and quantum physics to explore in depth the microscopic properties of physical systems and relate them to their macroscopic properties. These frameworks also allow to go beyond equilibrium situations. Given the notably increasing complexity of mathematical models to study realistic systems, and their coupling to their environment that constrains their dynamics, both analytical approaches and numerical methods that build on these models show limitations in scope or applicability. On the other hand, machine learning, i.e., data-driven, methods prove to be increasingly efficient for the study of complex quantum systems. Deep neural networks, in particular, have been successfully applied to many-body quantum dynamics simulations and to quantum matter phase characterization. In the present work, we show how to use a variational autoencoder (VAE)—a state-of-the-art tool in the field of deep learning for the simulation of probability distributions of complex systems. More precisely, we transform a quantum mechanical problem of many-body state reconstruction into a statistical problem, suitable for VAE, by using informationally complete positive operator-valued measure. We show, with the paradigmatic quantum Ising model in a transverse magnetic field, that the ground-state physics, such as, e.g., magnetization and other mean values of observables, of a whole class of quantum many-body systems can be reconstructed by using VAE learning of tomographic data for different parameters of the Hamiltonian, and even if the system undergoes a quantum phase transition. We also discuss challenges related to our approach as entropy calculations pose particular difficulties.
登录
查看更多内容
影响因子：
3.7
作者：
Choo, Kenny;Neupert, Titus;Carleo, Giuseppe
通讯作者：
Carleo, Giuseppe
影响因子：
19.6
作者：
Boixo, Sergio;Ronnow, Troels F.;Troyer, Matthias
通讯作者：
Troyer, Matthias
影响因子：
56.9
作者：
Carleo, Giuseppe;Troyer, Matthias
通讯作者：
Troyer, Matthias
影响因子：
2.4
作者：
Allahverdyan, Armen E.;Johal, Ramandeep S.;Mahler, Guenter
通讯作者：
Mahler, Guenter
影响因子：
23.8
作者：
Carrasquilla, Juan;Torlai, Giacomo;Aolita, Leandro
通讯作者：
Aolita, Leandro