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，是当代工程和物理的主要目标之一。使量子通信技术得以实现的关键理论突破是在20世纪30年代发现了量子纠缠现象，并意识到纠缠不仅代表着量子理论的好奇心，而且是一种关键资源，可以被利用来实现在20世纪80年代迄今不可能完成的通信任务。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为特定问题提供了比经典计算更大的效率优势，但人们既不知道这类问题的确切类别是什么，也不知道量子理论的一个或多个特定方面使这些优势是什么。然而，已经确定的QC的应用可能只是全部潜力的一小部分，因为只发现了少数几个量子算法。彼得·肖尔(Peter Shor)发现了第一个实用的量子算法，建立了现代量子计算机科学。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。”在没有清楚了解量子计算优势的基本量子现象的情况下寻找量子算法，我们是在黑暗中工作。尽管进行了数十年的研究，但使量子理论相对于经典计算机具有量子优势的关键特征仍然难以捉摸。量子理论的几个新奇特征-如纠缠、叠加和不协调--被提出为候选者，但后来被证明是不够的。最近的证据，例如由Rausendorff(Phys.牧师A，88)和霍华德等人。(自然，510)，证明了称为语境性的非局部性的泛化在QC中发挥着重要作用，并表明它可能是理解QC独特能力的关键。我们的愿景是深化语境理论，目标是实现对它在QC中所扮演的确切角色的理解，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处于独特的地位：PI是两个领先的情景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，专家团队包括负责将上下文与质量控制联系起来的初步证据的专家，以及量子算法和非局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.