Quantum Information-Constrained Optimal Transport

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The proposed research will be conducted through the collaboration with Prof. Sandeep Pradhan Sadanandarao from the University of Michigan. It aims to develop a new theory termed quantum information-constrained optimal transport, which unifies quantum rate-distortion theory and quantum transport theory, by leveraging the McMaster team's expertise on machine learning and the international collaborator's expertise on quantum information theory and quantum field theory. This new theory will shed light on a host of problems in the emerging field of quantum information science that can be modelled as transportation between source and destination through a bit pipeline. In particular, it will provide architectural principles for designing quantum machine learning systems with a digital interface. Such systems arise whenever one attempts to compress or transmit feature maps extracted by quantum machine learning algorithms. The conventional approach is to design the digital part (i.e., quantum compression and quantum communication) and the analog part (i.e., quantum machine learning) of such systems separately. As a consequence, the integrated system often suffers from significant performance degradation due to the mismatch between the digital part and the analog part. In the framework of quantum information-constrained optimal transport, these two parts are jointly considered from the very beginning, thus can live coherently in the resulting system. The proposed research also offers a systematic approach to empowering machine learning applications via quantum information processing, thus expedites the transition from classical machine learning to quantum machine learning. It will strengthen Canada's leadership in information theory, machine learning, and quantum physics research and provide more incentives for the exchange of ideas between these communities. The HQP trained through this project will develop solid technical skills across multiple disciplines, broad perspectives on information science and technology, and the ability to communicate their insights to others. They will be well equipped to stay at the forefront of the quantum revolution.