Aspects of Quantum Computational Universality in the Measurement-Based Models

有几种方法可以构建量子计算机，它们可能比今天的经典计算机更快地解决问题。一种被称为基于测量的量子计算的方法需要“资源状态”才能工作。资源态可以用量子力学系统，如离子、原子、分子、超导电路或称为光子的光的基本量子态来制造。然而，关于如何描述资源状态仍有几个悬而未决的问题。这个项目将探索不同类型的资源状态在噪音存在下是如何或多或少具有弹性的。该项目还将研究如何将固体中新发现的相用作资源状态。本研究项目的成果将通过开发表征量子计算资源的方法，以及在材料科学和量子信息科学之间建立智力联系来促进进展。该项目还将训练学生开发量子计算机的新资源和设计。与经典计算机相比，量子计算机在某些任务上具有指数级的加速。为了实现这一点，这里研究的设计，如基于测量的量子计算模型，使用高度纠缠态的局部测量。因此，纠缠是一种资源。然而，关于这种类型的资源仍然存在几个基本问题。例如，除了群集状态及其泛化之外，还不知道还有哪些其他状态或其他类型的纠缠可以支持通用量子计算。量化某些资源状态比其他资源状态提供更强的抗噪声能力的程度也很重要。这个项目将解决这些问题。它还将研究资源状态是否可以从物质的某些阶段产生。例如，最近在凝聚态物理中发现的一些物质状态具有拓扑秩序，要么是固有的，要么是受对称性保护的，这可能是量子计算的资源。更具体地说，将研究一维、二维和三维空间中的各种对称保护拓扑有序状态（以及二维空间中的固有拓扑有序状态），以确定它们是否通过构建新的量子门或通过局部测量减少到已知类型的资源状态来实现量子计算。将描述使用这些状态进行计算的物理特性。此外，还将研究这些具有特定拓扑属性的资源状态是否可以导致新的容错方案。该项目的成果将在量子信息科学和凝聚态物理之间建立进一步的联系，并将有助于完全表征量子计算的通用资源的挑战。这将有助于设计可可靠实验实现的量子信息处理系统。

There are several approaches for building quantum computers that will potentially solve problems faster than today's classical computers. One approach, called measurement-based quantum computation, requires "resource states" in order to work. Resource states can be made with quantum mechanical systems such as ions, atoms, molecules, superconducting circuits, or elementary quantum states of light called photons. Yet there are still several open questions about how to characterize resource states. This project will explore how different types of resource states are more or less resilient in the presence of noise. The project will also study how newly discovered phases in solids can be used as a resource states. The outcomes of this research project will promote progress by developing methods to characterize resources for quantum computation, and establishing intellectual connections between materials science and quantum information science. This project will also train students to develop new resources and designs for quantum computers. Quantum computers boast exponential speedup for certain tasks compared to classical computers. To realize this, designs studied here such as measurement-based models of quantum computation use local measurements on highly entangled states. Entanglement is thus a resource. However there are still several fundamental questions about this type of resource. For example, in addition to the cluster state and its generalization, it is not known what other states or other types of entanglement can support universal quantum computation. It is also important to quantify the extent to which some resource states provide more resistance to noise than others. This project will address those questions. It will also investigate if resource states can emerge from certain phases of matter. For example some states of matter recently found in condensed-matter physics possess topological order, either intrinsic or that protected by symmetry, that may serve as a resource for quantum computing. More specifically, various symmetry-protected topologically ordered states in one, two, and three spatial dimensions (and intrinsic topological order states in two dimensions) will be studied to see whether they enable quantum computation via construction of new quantum gates, or reduction by local measurement to known types of resource states. Physical properties that enable computation using these states will be characterized. Furthermore, the question of whether these resource states with certain topological properties can lead to new fault-tolerant schemes will be investigated. The outcomes of the project will establish further connections between ideas in quantum information science and condensed-matter physics, and will contribute to the challenge of completely characterizing universal resources for quantum computations. This will contribute to progress designing quantum information processing systems that can be reliably experimental realized.