The University of California, Berkeley has received a $600,000 Project Grant award from the National Science Foundation's (NSF) Computer and Information Science and Engineering (CISE) Federal Grant Program (CFDA 47.070) to conduct research into network expansion and quantum computing. The overarching goals of the project are to investigate the optimal tradeoff between network sparsity and mixing rates, as well as to advance the understanding of quantum generalizations of expansion. Key technical elements include: (a) exploring the existence of optimally expanding non-bipartite "Ramanujan" graphs; (b) constructing optimal error-correcting "epsilon-biased codes" through studying random walks on Ramanujan and related graphs; and (c) proving rapid mixing for quantum Markov chains converging to thermal states of quantum systems. The project runs from August 1, 2024 to July 31, 2027 and aims to uncover new mathematical connections between theoretical computer science, error-correcting codes, cryptography, quantum computation, and statistical mechanics.
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