Fast counting with tensor networks

TL;DR

This paper presents tensor network contraction algorithms for efficiently counting solutions to complex constraint satisfaction problems, outperforming existing solvers on certain #P-hard problems.

Contribution

It introduces a novel tensor network approach for #CSP counting and develops heuristics that improve performance on challenging #SAT problems.

Findings

Outperforms state-of-the-art solvers on #SAT problems

Uses tensor networks to represent #CSP formulas

Employs graph-theoretical heuristics for contraction order

Abstract

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.