the Mathematics of Quantum Computation

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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.