Machine Learning as the Interface Between Quantum and Classical Computation

由于多体量子系统在维数上的指数标度，使用经典计算机研究大型甚至中型量子系统可能被证明是困难的。这对自然发生的量子力学现象的模拟和研究以及量子计算的发展都有影响。我们已经达到了这样一个阶段，即存在足够大的量子模拟器，使用标准计算技术对它们进行经典模拟和分析是不可行的。在将机器学习思想应用于量子物理研究中，已经发现了这些方法的一个有前途的替代方案。人工神经网络的隐藏/可见层结构提供了足够的表征能力来描述量子态（导致“神经网络状态”），但对于一般状态，这仍然需要不可行的计算资源。机器学习技术可以描述量子态的系统的大小在许多情况下可以大大超过经典计算的可能性，因此机器学习可以被认为是经典和量子计算之间的“接口”。找到量子态的有效表示的问题已经以多种方式处理，并且对于某些系统，存在对状态的高度压缩描述（例如张量网络，MPS）。最近的工作表明，用测量数据训练的神经网络状态也可以提供许多物理状态的有效表示，然而，神经网络选择的自由度提出了几个目前悬而未决的问题。通过这种方式，神经网络状态为量子态层析成像提供了一个有用的工具，允许人们从一组测量数据中重新创建量子态。神经网络状态的一个越来越受欢迎的选择是受限玻尔兹曼机（RBM），它在学习许多状态方面表现出巨大的潜力，同时也能够科普一定程度的远程纠缠。该项目旨在研究RBM用于断层扫描的代表性能力，并试图确定在多大的尺寸和纠缠度下，该代表性不再有效。然后，这些机器学习技术将被应用于在IBM的一些原型量子处理器上进行断层扫描，以展示这一概念的实际效用，并量化这些处理器的性能。

Due to the exponential scaling in the dimensionality of many-body quantum systems, the study of large and even intermediate sized quantum systems using classical computers can prove intractable. This has ramifications in both the simulation and study of naturally occurring quantum mechanical phenomena and in the development of quantum computing. We have reached the stage where there exist quantum simulators of great enough size that performing classical simulation and analysis of them is unfeasible using standard computational techniques. A promising alternative to these methods has been found in applying machine learning ideas to the study of quantum physics. The hidden/visible layer structure of artificial neural networks provides sufficient representational power to describe quantum states (resulting in a "neural network state") but for generic states this still requires unfeasible computational resources. The size of system at which machine learning techniques can describe a quantum state can in many cases vastly outmatch what is otherwise possible with classical computation and so machine learning could be thought of as the "interface" between classical and quantum computation. The problem of finding an efficient representation for a quantum state has been approached in numerous ways and for some systems there exist highly compressed descriptions of the states (E.G. tensor networks, MPS). Recent work has shown that neural network states trained with measurement data can also provide efficient representations of many physical states, however freedom in the choice of neural network poses several currently open questions. In this way neural network states provide a useful tool for quantum state tomography, allowing one to recreate a quantum state from a set of measurement data. An increasingly popular choice of neural network state is the Restricted Boltzmann Machine (RBM) which has shown great potential in learning many states while also being able to cope with a degree of long-range entanglement. This project aims to investigate the representational power of RBMs for tomography and attempt to determine at what size and level of entanglement of the system in question does the representation cease to be efficient. These machine learning techniques will then be applied in performing tomography on some of IBMs prototype quantum processors to both demonstrate the practical utility of this concept and quantify the performance of these processors.