Contextuality as a Resource in Quantum Computation

实现量子理论在信息处理中的应用潜力，包括量子通信和量子计算，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20世纪30年代量子纠缠现象的发现，以及20世纪80年代人们认识到纠缠不仅代表了量子理论的好奇心，而且是一种可以用来实现迄今为止不可能实现的通信任务的关键资源。贝尔在20世纪60年代将量子非定域性确定为纠缠的本质量子方面。虽然人们普遍认为量子计算在特定问题上提供了比经典计算更大的效率优势，但人们既不知道这些问题的确切类别是什么，也不知道量子理论的具体方面是什么，也不知道这些优势是什么。然而，已经确定的QC应用可能只是全部潜力的一小部分，因为只有少数量子算法被发现。彼得·肖尔（Peter Shor）发现了第一个实用的量子算法，开创了现代量子计算机科学，他思考了为什么量子算法被发现的这么少，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明确概念的情况下，寻找量子算法，我们是在黑暗中工作。尽管经过数十年的研究，量子理论使量子优于经典计算机的关键特征仍然难以捉摸。量子理论的几个新特征——如纠缠、叠加和不和谐——已经被提出作为候选，但随后被证明是不够的。最近的证据，如劳森多夫（物理学家）提供的。Rev. A, 88)和Howard等人（Nature, 510）证明了称为情境性的非局部性的概括在QC中起着重要作用，并表明它可能是理解QC独特能力的关键。我们的愿景是深化情境理论，目标是理解它在QC中扮演的确切角色，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具有独特的优势：pi是两个领先的情境性理论框架的共同发明者。我们将通过与一个国际的、跨学科的专家团队合作来实现我们的目标，包括那些负责将情境性和质量控制联系起来的初始证据的专家，以及量子算法和非定域性资源理论的公认领导者。

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.