Harnessing Symmetry-Protected Topological Orders for Quantum Computation

利用对称保护的拓扑序进行量子计算

• 批准号: 1620651
• 负责人: Akimasa Miyake
• 金额: $ 19.5万
• 依托单位: University of New Mexico
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-09-15 至 2020-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1620651&HistoricalAwards=false
• 关键词: Harnessing; Symmetry; Protected; Topological; Orders

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.

计算机在现代社会中已经变得无处不在和不可或缺，并且对新的和更强大的计算机的搜索是不断的。 探索的途径之一是开发基于量子信息处理（QIP）的计算。QIP利用量子态，例如电子的自旋，来编码信息。诸如“叠加”和“纠缠”的量子效应使得QIP设备能够处理具有超出传统的黑或白色（所谓的0或1）逻辑的灰色阴影的信息，并且相对于传统设备获得显著的改进。然而，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个类别。该项目的目标是利用超导和磁性等多体量子物理现象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折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，该项目将探索如何使用宏观量子序在计算和模拟中获得一些量子优势。这项研究将有助于建立量子信息科学的知识基础，并有助于培养这一高度跨学科和迅速扩展的领域的未来科学家。基于测量的量子计算（MQC）框架是研究量子优势起源的一种方便方法，例如量子加速计算。 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自然地发现在受挫折的量子自旋系统的量子自旋液相中，称为受保护的拓扑序（SPTO），可以用作MQC的资源。 这个项目将探索如何通过使用更高维的SPTO获得更高层次的纠缠和更内在的量子门复杂性（Clifford层次）。2D SPTO的新纠缠具有传统的通用纠缠所不具备的几个特征（如SPTO具有1D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。该项目利用宏观量子序与量子复杂性之间的这种具体联系来探讨量子计算和模拟中有关可扩展性和非经典复杂性的关键问题。因此，它建立了两个研究领域之间的联系：量子信息科学和量子多体物理学。