Fast counting with tensor networks

doi:10.21468/scipostphys.7.5.060

Fast counting with tensor networks

2019-11-12

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DOI：10.21468/scipostphys.7.5.060

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We introduce tensor network contraction algorithms for counting satisfying assignments of constraint satisfaction problems (#CSPs). We represent each arbitrary #CSP formula as a tensor network, whose full contraction yields the number of satisfying assignments of that formula, and use graph theoretical methods to determine favorable orders of contraction. We employ our heuristics for the solution of #P-hard counting boolean satisfiability (#SAT) problems, namely monotone #1-in-3SAT and #Cubic-Vertex-Cover, and find that they outperform state-of-the-art solvers by a significant margin.

Fast counting with tensor networks

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