Quantum Machine Learning, Error Correction, and Topological Phases of Matter

Abstract

Quantum computation is an exciting and rapidly developing paradigm of computing, which has the potential to improve or accelerate numerous important applications ranging from cryptography to drug discovery. Inspired by these prospects, researchers and engineers across the world have, in recent years, made tremendous advances in building programmable quantum devices. Nevertheless, the size and error rates in state-of-the-art quantum computers are still several orders of magnitude away from those required to achieve computational speedups using existing quantum algorithms. These developments, along with their limitations, motivate us to consider two important questions: First, are there any useful applications in which current or near-term quantum devices can outperform classical computers? Second, can we develop efficient error-correction schemes to suppress the error rates in near-term quantum devices?

In this dissertation, we present novel solutions to both of these questions. To address the first question, we identify an important class of problems in condensed-matter physics, namely the identification and characterization of quantum phases of matter, as one promising application of current and near-term quantum information processors. We develop new algorithms for using such quantum devices to solve these problems, and we demonstrate how our methods substantially outperform existing approaches. In addition, we respond to the second question by developing hardware-efficient quantum error correction protocols. By leveraging the distinctive properties and advantages of a given experimental setup to overcome its particular limitations, our proposals significantly reduce the number of quantum bits and operations required for performing quantum error correction and fault-tolerant quantum computation. Together, the works in this dissertation thus pave the way for the near-term realization of quantum computational advantages.