9,242 research outputs found

    Solving the Shortest Vector Problem in Lattices Faster Using Quantum Search

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    By applying Grover's quantum search algorithm to the lattice algorithms of Micciancio and Voulgaris, Nguyen and Vidick, Wang et al., and Pujol and Stehl\'{e}, we obtain improved asymptotic quantum results for solving the shortest vector problem. With quantum computers we can provably find a shortest vector in time 21.799n+o(n)2^{1.799n + o(n)}, improving upon the classical time complexity of 22.465n+o(n)2^{2.465n + o(n)} of Pujol and Stehl\'{e} and the 22n+o(n)2^{2n + o(n)} of Micciancio and Voulgaris, while heuristically we expect to find a shortest vector in time 20.312n+o(n)2^{0.312n + o(n)}, improving upon the classical time complexity of 20.384n+o(n)2^{0.384n + o(n)} of Wang et al. These quantum complexities will be an important guide for the selection of parameters for post-quantum cryptosystems based on the hardness of the shortest vector problem.Comment: 19 page

    Advances in quantum machine learning

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    Here we discuss advances in the field of quantum machine learning. The following document offers a hybrid discussion; both reviewing the field as it is currently, and suggesting directions for further research. We include both algorithms and experimental implementations in the discussion. The field's outlook is generally positive, showing significant promise. However, we believe there are appreciable hurdles to overcome before one can claim that it is a primary application of quantum computation.Comment: 38 pages, 17 Figure
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