Higher Algebra and Quantum Protocols

高等代数和量子协议

• 批准号: EP/S018883/1
• 负责人: Christopher Douglas
• 金额: $ 63.03万
• 依托单位: University of Oxford
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2019
• 资助国家: 英国
• 起止时间: 2019 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FS018883%2F1
• 关键词: Higher; Algebra; Quantum; Protocols

This research project will integrate expertise in the Oxford Mathematical Institute and the Birmingham School of Computer Science to build theoretical and practical tools for higher-dimensional algebraic computations in geometry and quantum information science. Through a structured research agenda, we will formulate the first combinatorial language of higher categories that is amenable to computer implementation and admits a natural geometric calculus, providing a natural setting to investigate modern questions in higher representation theory, quantum algebra, and quantum computation. We will then design and build a computer implementation of this language and thereby create a research and proof assistant that natively allows the exploration and verification of complex manipulations of high-dimensional structures. Finally we will apply this computational tool to generalise structures in quantum algebra, yielding novel protocols in quantum information, such as quantum error correction of nonplanar states.This research effort will be organised into four strands---Foundations, Computer Implementation, Graphical Calculus, and Quantum Protocols---and the ambitious, integrated research agenda will be achieved by uniting researchers across the two institutions and disciplines, and by actively engaging with the broader scientific community.

该研究项目将整合牛津数学研究所和伯明翰计算机科学学院的专业知识，为几何和量子信息科学中的高维代数计算构建理论和实践工具。通过结构化的研究议程，我们将制定第一个适合计算机实现的高级类别组合语言，并承认自然几何演算，为研究高级表示理论，量子代数和量子计算中的现代问题提供自然环境。然后，我们将设计并构建该语言的计算机实现，从而创建一个研究和证明助手，该助手可以在本地探索和验证高维结构的复杂操作。最后，我们将应用该计算工具来推广量子代数中的结构，从而产生量子信息中的新协议，例如非平面态的量子纠错。这项研究工作将被组织成四个部分——基础、计算机实现、图形演算和量子协议——雄心勃勃的综合研究议程将通过联合两个机构和学科的研究人员，并积极参与更广泛的科学界来实现。

项目成果

Framed Combinatorial Topology

框架组合拓扑

• 发表时间: 2021
• 作者: C Dorn

Fusion 2-categories and a state-sum invariant for 4-manifolds

• 发表时间: 2018-12
• 期刊: arXiv: Quantum Algebra
• 作者: Christopher L. Douglas;David J. Reutter

Manifold diagrams and tame tangles

流形图和驯服的缠结

• DOI: 10.48550/arxiv.2208.13758
• 发表时间: 2022
• 期刊: arXiv e-prints
• 作者: Dorn Christoph

Conformal nets V: dualizability

共形网络 V：对偶性

• DOI: 10.48550/arxiv.1905.03393
• 发表时间: 2019
• 期刊: arXiv e-prints
• 作者: Bartels Arthur