Collaborative Research: Adiabatic Quantum Computing and Statistics

几十年来，根据所谓的摩尔定律，计算机能力按不变成本翻了一番，大约每两年一次。这一梦想的实现是通过计算机硬件制造技术的进步，使电子设备变得越来越小。然而，随着计算机电子设备的尺寸接近原子尺度，量子效应开始干扰它们的功能，因此传统的计算机技术方法遇到了尺寸限制的根本困难。这项研究项目涉及量子计算，这是一种依赖于量子物理原理的计算机技术的发展，而不是传统计算机使用的遵循经典物理定律的电子设备。这一革命性的领域将使一系列奇异的新设备成为可能，特别是它可能会导致强大的量子计算机的创造。该研究项目是正在开发量子技术和建造具有超过经典计算设备能力的量子设备的前沿研究努力之一。量子计算和量子信息科学更普遍地关注物理系统的量子态的准备和控制，以操纵和传输信息。量子系统的复杂性通常随其大小呈指数增长。因此，在经典计算机上存储量子系统的状态需要指数级的比特存储，通过经典计算机模拟量子系统面临着巨大的计算挑战。另一方面，由于量子系统能够存储和跟踪指数数的复数，并随着系统的发展执行数据处理和计算，因此量子系统作为计算工具前景广阔。量子信息科学正在努力理解如何利用隐藏在量子系统中的大量信息，并利用原子和光子的巨大潜在计算能力来进行信息处理和计算。这个跨学科的研究项目解决了量子信息科学中关于量子计算和机器学习之间的接口以及量子断层扫描和压缩传感之间的问题。这项合作研究旨在探索绝热量子计算的力量及其对计算机科学和统计学的影响，特别是机器学习和蒙特卡洛抽样。这项工作研究了计算机科学和统计学中的机器学习、应用数学、统计学和工程学中的压缩传感以及量子物理中的量子层析成像在绝热量子计算中的领先技术的使用。研究活动促进了具有不同学科背景的研究人员之间的合作，并激发了可能的突破性、变革性研究的新想法。

For decades computer power has doubled for constant cost roughly once every two years according to the so-called Moore's law. This dream run is realized through technological advances in the fabrication of computer hardware, making electronic devices smaller and smaller. However, as the sizes of the computer electronic devices get close to the atomic scale, quantum effects are starting to interfere in their functioning, and thus conventional computer technology approaches run up against fundamental difficulties of size limit. This research project concerns quantum computing, the development of computer technology dependent on the principles of quantum physics, as opposed to the electronic devices following laws of classical physics used by classical computers. This revolutionary field will enable a range of exotic new devices, and in particular it will likely lead to the creation of powerful quantum computers. The research project is among the frontier research endeavors where quantum technologies are being developed and quantum devices are being built with capabilities exceeding those of classical computational devices. Quantum computation and quantum information science more generally concern the preparation and control of the quantum states of physical systems to manipulate and transmit information. A quantum system usually has complexity exponentially increasing with its size. As a result, it takes an exponential number of bits of memory on a classical computer to store the state of a quantum system, and simulations of quantum systems via classical computers face great computational challenge. On the other hand, since quantum systems are able to store and track an exponential number of complex numbers and perform data manipulations and calculations as the systems evolve, quantum systems hold great promise as computational tools. Quantum information science grapples with understanding how to take advantage of the enormous amount of information hidden in the quantum systems and to harness the immense potential computational power of atoms and photons for the purpose of information processing and computation. This cross-disciplinary research project addresses questions in quantum information science on the interface between quantum computing and machine learning and between quantum tomography and compressed sensing. The collaborative research aims to explore the power of adiabatic quantum computation and its impact on computer science and statistics in general and machine learning and Monte Carlo sampling in particular. The work investigates the use of leading techniques from machine learning in computer science and statistics, compressed sensing in applied mathematics, statistics, and engineering, and quantum tomography in quantum physics for adiabatic quantum computing. The research activities promote collaborations among investigators with different disciplinary backgrounds and stimulate novel ideas for possible breakthrough, transformative research.