Aspects of Quantum Computational Universality in the Measurement-Based Models

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.