Harnessing Symmetry-Protected Topological Orders for Quantum Computation

计算机在现代社会中已经变得无处不在，不可或缺，人们不断地寻找新的、功能更强大的计算机。探索的途径之一是发展基于使用量子信息处理(QIP)的计算。QIP利用量子态的优势，例如电子的自旋，来编码信息。量子效应，如“叠加”和“纠缠”，使QIP设备能够处理超出传统黑白(所谓的0或1)逻辑的灰度级信息，并实现对传统设备的重大改进。然而，要实现以QIP为基础的制度的目标，存在两大挑战。一个是在最近用少量量子比特进行的实验的基础上，找到扩大QIP设备规模的方法。另一个挑战是发现QIP设备在信息任务方面超过传统设备的更多例子和完整类别。这个项目的目标是利用研究超导和磁性等多体量子物理现象的想法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。更广泛地说，该项目将探索利用宏观量子秩序在计算和模拟中获得一些量子优势的方法。这项研究将有助于建立量子信息科学的知识基础，并为这一高度交叉和迅速发展的领域培养未来的科学家。基于测量的量子计算(MQC)框架是研究计算中量子加速等量子优势来源的便捷途径。MQC需要纠缠态作为一种资源。这个项目将研究如何将某些类型的宏观纠缠用作MQC的资源，这些纠缠自然地存在于受挫量子自旋系统的量子自旋液体相中，称为对称保护拓扑有序(SPTO)。这个项目将探索如何通过使用更高维的SPTO来获得更高水平的纠缠，以及更本征的量子门复杂性(Clifford层次)。由2D SPTO产生的新纠缠具有几个传统的普适纠缠所不具备的特征(就像SPTO是一维性质的团簇状态)，相反，即使通过最简单的单自旋X、Y和Z测量，它也能够进行普适量子计算。本项目利用宏观量子序与量子复杂性之间的这种具体联系，探讨量子计算和模拟中的可扩展性和非经典复杂性等关键问题。因此，它在两个研究领域之间建立了联系：量子信息科学和量子多体物理。

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.