Harnessing Symmetry-Protected Topological Orders for Quantum Computation

在现代社会中，计算机已经变得无处不在，不可或缺，人们一直在寻找新的、更强大的计算机。探索的一个途径是发展基于量子信息处理（QIP）的计算。QIP利用量子态（例如电子的自旋）来编码信息。“叠加”和“纠缠”等量子效应使QIP设备能够处理灰色阴影的信息，超越传统的非黑即白（所谓的0或1）逻辑，并获得比传统设备的巨大改进。然而，要实现基于qip的系统的目标，存在两个主要挑战。一个是在最近的少量量子比特实验的基础上，找到扩大QIP设备规模的方法。另一个挑战是发现更多的例子，以及QIP设备超越传统设备的信息任务的整体类别。该项目的目标是利用多体量子物理现象（如超导性和磁性）研究中的思想来解决这些关键问题，例如，表现出奇异磁性的受挫量子自旋系统如何也具有作为量子计算机的内在能力。更一般地说，本项目将探索如何利用宏观量子顺序在计算和模拟方面获得一些量子优势。这项研究将有助于建立量子信息科学的知识库，并在这个高度跨学科和快速发展的领域培养未来的科学家。基于测量的量子计算（MQC）框架为研究量子计算中的量子加速等量子优势的起源提供了一种方便的方法。MQC需要纠缠态作为资源。该项目将研究如何将某些类型的宏观纠缠作为MQC的资源，这些纠缠自然存在于被称为对称保护拓扑秩序（SPTO）的受挫量子自旋系统的量子自旋液相中。该项目将探索如何通过使用高维SPTO获得具有更多内在量子门复杂性（Clifford层次）的更高层次的纠缠。二维SPTO的新纠缠具有传统通用纠缠所不具备的几个特征（比如其SPTO具有一维性质的簇态），并且相比之下，即使通过最简单的单自旋X， Y和Z测量也能够进行通用量子计算。本项目利用宏观量子顺序和量子复杂性之间的具体联系，探讨量子计算和模拟中可扩展性和非经典复杂性的关键问题。从而在量子信息科学和量子多体物理两个研究领域之间建立起联系。

Computers have become ubiquitous and indispensable in modern society, and the search for new and more powerful computers is constant. One avenue of exploration is to develop computation based on using quantum information processing (QIP). QIP takes advantage of quantum states, for instance spins of electrons, to encode information. Quantum effects such as "superposition" and "entanglement" enable QIP devices to process information with shades of gray beyond the conventional black-or-white (so-called 0-or-1) logic, and to attain drastic improvements over conventional devices. However, there are two major challenges to achieving the goal of a QIP-based system. One is to find ways to scale up QIP devices, building on recent experiments with small numbers of quantum bits. The other challenge is to discover more examples, and whole categories, of informational tasks for which QIP devices surpass conventional devices. The goal of this project is to address these key issues using ideas from the study of many-body quantum physics phenomena such as superconductivity and magnetism, as, for example, how frustrated quantum spin systems that exhibit exotic magnetism also possess intrinsic capability as a quantum computer. In more general terms, the project will explore ways to use macroscopic quantum order to obtain some quantum advantage in computation and simulation. This research will contribute to the knowledge base of quantum information science and to the training of future scientists in this highly interdisciplinary and rapidly expanding field.The framework of measurement-based quantum computation (MQC) is a convenient way to study the origin of quantum advantages such as quantum speed-up in computation. MQC needs entangled states as a resource. This project will examine how certain types of macroscopic entanglement which are naturally found in quantum spin liquid phases of frustrated quantum spin systems called symmetry-protected topological orders (SPTO) can be used as a resource for MQC. This project will explore how a higher level of entanglement with more intrinsic quantum-gate complexity (Clifford hierarchy) is available by using higher-dimensional SPTO. The new entanglement by 2D SPTO has several features which are not available by conventional universal entanglement (like the cluster state whose SPTO is of a 1D nature), and is in contrast capable of universal quantum computation even by simplest single-spin X, Y, and Z measurements. This project takes advantage of this concrete connection between macroscopic quantum orders and quantum complexity to approach the key issues about scalability and non-classical complexity in quantum computation and simulation. Thus it builds connections between two research fields: quantum information science and quantum many-body physics.