Machine Learning as the Interface Between Quantum and Classical Computation

点击翻译按钮获取中文摘要

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.