Contextuality as a Resource in Quantum Computation

上下文作为量子计算中的资源

• 批准号: EP/N018745/1
• 负责人: Samson Abramsky
• 金额: $ 40.82万
• 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: 2016
• 资助国家: 英国
• 起止时间: 2016 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FN018745%2F1
• 关键词: Contextuality; Resource; Quantum; Computation

Realizing the potential of applications of quantum theory to information processing, which include quantum communication and quantum computation, is one of the primary goals of contemporary engineering and physics. The key theoretical breakthroughs enabling quantum communication technologies were the discovery of the phenomenon of quantum entanglement in the 1930s and the realisation that entanglement represented not merely a curiosity of quantum theory but a critical resource which could be exploited to achieve heretofore impossible communication tasks in the 1980s. Bell indentified quantum nonlocality as the essentially quantum aspect of entanglement in the 1960s. While it is widely understood that quantum computation offers substantial efficiency advantages over classical computation for particular problems, it is neither understood what the precise class of such problems is nor what the particular aspect or aspects of quantum theory enabling these advantages are. The applications for QC which have been identified are likely only a fraction of the full potential, however, as only a handful of quantum algorithms have been discovered. Peter Shor, whose discovery of the first practical quantum algorithm founded modern quantum computer science, contemplated why so few quantum algorithms have been discovered and suggested that, "quantum computers operate in a manner so different from classical computers that our techniques for designing algorithms and our intuitions for understanding the process of computation no longer work". In seeking quantum algorithms without a clear idea of the essential quantum phenomenon accounting for quantum computational advantage, we are working in the dark.Despite decades of research, the key feature of quantum theory enabling quantum advantage over classical computers remains elusive. Several of quantum theory's novel features---such as entanglement, superposition, and discord---have been proposed as candidates but have subsequently proven insufficient. Recent evidence, such as that provided by Rausendorff (Phys. Rev. A, 88) and Howard et al. (Nature, 510), demonstrates that a generalization of nonlocality called contextuality plays an important role in QC and suggests that it is, perhaps, a sought-after key to understanding the unique capabilities of QC. Our vision is to deepen the theory of contextuality with the goals of achieving an understanding of the precise role it plays in QC and how it is a resource for computational advantage. Our team is uniquely positioned to tackle this challenge: the PIs are co-inventors of the two leading theoretical frameworks for contextuality. We will achieve our goal by collaborating with an international, interdisciplinary team of experts including those responsible for the initial evidence linking contextuality and QC as well as recognized leaders in quantum algorithms and the resource theory of nonlocality.

实现量子理论在信息处理（包括量子通信和量子计算）中应用的潜力是当代工程和物理学的主要目标之一。实现量子通信技术的关键理论突破是在 20 世纪 30 年代发现了量子纠缠现象，并认识到纠缠不仅代表了量子理论的好奇心，而且是一种关键资源，可用于在 20 世纪 80 年代实现迄今为止不可能的通信任务。贝尔在 20 世纪 60 年代将量子非定域性视为纠缠的本质量子方面。虽然人们普遍认为，对于特定问题，量子计算比经典计算具有显着的效率优势，但人们既不了解此类问题的精确类别是什么，也不了解量子理论实现这些优势的特定方面是什么。然而，由于只发现了少数量子算法，因此已确定的质量控制应用可能只是全部潜力的一小部分。彼得·肖尔（Peter Shor）发现了第一个实用的量子算法，奠定了现代量子计算机科学的基础，他思考了为什么发现的量子算法如此之少，并提出“量子计算机的运行方式与经典计算机如此不同，以至于我们设计算法的技术和理解计算过程的直觉不再起作用”。在对量子计算优势的基本量子现象没有清晰概念的情况下寻求量子算法时，我们是在黑暗中工作。尽管经过了数十年的研究，量子理论相对于经典计算机的量子优势的关键特征仍然难以捉摸。量子理论的一些新特征——例如纠缠、叠加和不和谐——已被提议作为候选特征，但随后被证明是不够的。最近的证据，例如 Rausendorff (Phys. Rev. A, 88) 和 Howard 等人提供的证据。 （Nature，510）表明，称为上下文的非定域性概括在质量控制中发挥着重要作用，并表明它可能是理解质量控制独特功能的广受欢迎的关键。我们的愿景是深化情境性理论，目标是了解它在质量控制中发挥的精确作用以及它如何成为计算优势的资源。我们的团队在应对这一挑战方面拥有独特的优势：PI 是两个领先的情境性理论框架的共同发明者。我们将通过与国际跨学科专家团队合作来实现我们的目标，其中包括负责关联情境性和质量控制的初始证据的专家以及量子算法和非局域性资源理论领域公认的领导者。

项目成果

A complete characterisation of All-versus-Nothing arguments for stabiliser states

稳定态的“全与无”论证的完整表征

• DOI: 10.48550/arxiv.1705.08459
• 发表时间: 2017
• 作者: Abramsky S

Possibilities Determine the Combinatorial Structure of Probability Polytopes

• DOI: 10.1016/j.jmp.2016.03.006
• 发表时间: 2016-03
• 期刊: ArXiv
• 作者: S. Abramsky;Rui Soares Barbosa;K. Kishida;Raymond Lal;Shane Mansfield

Contextuality from Quantum Physics to Psychology

从量子物理学到心理学的语境

• DOI: 10.1142/9789814730617_0002
• 发表时间: 2016
• 作者: Abramsky S

Minimum Quantum Resources for Strong Non-Locality

• DOI: 10.4230/lipics.tqc.2017.9
• 发表时间: 2017-05
• 作者: S. Abramsky;Rui Soares Barbosa;Giovanni Carù;Nadish de Silva;K. Kishida;Shane Mansfield

Whither semantics?

语义在哪里？

• DOI: 10.1016/j.tcs.2019.06.029
• 发表时间: 2020
• 期刊: Theoretical Computer Science
• 影响因子: 1.1
• 作者: Abramsky S