the Mathematics of Quantum Computation

量子计算(QC)是一种直接基于量子力学第一原理的计算新范式。虽然传统智慧长期以来一直认为量子物体的反直觉和随机行为将阻碍计算机器的构建，但最近人们意识到，一旦得到适当的利用，它们实际上可以成为强大的资源。有朝一日，使用QC解决超出任何传统计算机能力的计算问题将成为可能，也就是实现“量子优势”。QC改变我们生活的方方面面--从国家安全到物流；气候和金融预测；材料和药物设计--的潜力已经引发了大量的政府和商业投资。然而，关于量子计算机能力的许多最基本的问题还没有得到回答。目前还不清楚量子计算机如何以及为哪些问题提供了任何优势。实现量子优势的量子理论的关键特征是什么？答案将澄清量子计算机产生重大好处的一组问题，并促进解决这些问题所需的新量子算法的开发。它还将使量子计算机的最佳效率设计成为可能，从而加速它们的建造。德席尔瓦的研究旨在通过结合物理学、计算机科学和纯数学的思想和工具来回答这个基本问题。他将专注于发展一个新兴的令人兴奋的假设，即从量子力学的基础上提出的一个概念--“背景”是实现量子优势的关键资源。最近，语境性和数理逻辑之间的丰富联系已经被揭示：我们现在理解了逻辑悖论存在于语境性的核心。德·席尔瓦博士正在采取一种独特的方法，利用这些联系来解释量子优势。德席尔瓦将通过将量子理论的悖论与量子计算机的能力联系起来，并提供释放QC全部潜力所需的计算优势的清晰、高水平的描绘，来实现这一点。因此，量子计算机将被更快地构建起来，并能够解决比目前认为可能的更多的问题。因此，加拿大将获得在这一新兴行业中处于领先地位的经济利益，以及在所有科学领域进行创新的技术利益。

Quantum computation (QC) is a new paradigm of computing that is based directly on quantum mechanical first principles. While conventional wisdom had long held that the counterintuitive and random behaviours of quantum objects would be a hindrance to the construction of computational machines, it was recently realized that they can, in fact, be powerful resources once properly harnessed. It will one day be possible to solve computational problems using QC that are beyond the capabilities of any conventional computer i.e. achieve 'quantum advantage'.The potential of QC to transform every aspect of our lives-from national security to logistics; climate and financial prediction; material and pharmaceutical design-has triggered massive governmental and commercial investment. However, many of the most basic questions about the power of quantum computers are yet to be answered. It is not known exactly how and for which problems quantum computers offer any advantage. What are the key features of quantum theory that enable quantum advantage? The answer will clarify the set of problems for which quantum computers yield a significant benefit and facilitate the development of new quantum algorithms required to solve them. It will also enable the optimally efficient design of quantum computers and thereby hasten their construction.Dr. de Silva's research aims to answer this fundamental question by combining ideas and tools from physics, computer science, and pure mathematics. He will focus on developing the emerging and exciting hypothesis that 'contextuality', a concept from the foundations of quantum mechanics, is a key resource for achieving quantum advantage. Recently, rich connections between contextuality and mathematical logic have been uncovered: we now understand that logical paradoxes lie at the heart of contextuality. Dr. de Silva is taking the unique approach of utilizing these connections to explain quantum advantage.Dr. de Silva will achieve this this by connecting the paradoxes of quantum theory to the power of quantum computers and providing the clear, high-level delineation of computational advantage needed to unlock the full potential of QC. Quantum computers will thereby be constructed sooner and be capable of solving more problems than currently thought possible. As a result, Canada will reap the economic benefits of leadership in this emerging industry and the technological benefits of innovation across all areas of science.