## SciPost Submission Page

# Fast counting with tensor networks

### by Stefanos Kourtis, Claudio Chamon, Eduardo R. Mucciolo, Andrei E. Ruckenstein

### Submission summary

As Contributors: | Stefanos Kourtis |

Preprint link: | scipost_201908_00005v1 |

Date submitted: | 2019-08-05 |

Submitted by: | Kourtis, Stefanos |

Submitted to: | SciPost Physics |

Domain(s): | Theor. & Comp. |

Subject area: | Condensed Matter Physics - Computational |

### 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.

###### Current status:

Editor-in-charge assigned

### Submission & Refereeing History

Submission scipost_201908_00005v1 on 5 August 2019

## Reports on this Submission

### Anonymous Report 1 on 2019-8-25 Invited Report

### Report

The paper seems to be written well and discussions are convincing. I recommend the publication.