## SciPost Submission Page

# Fast counting with tensor networks

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

#### This is not the current version.

### Submission summary

As Contributors: | Stefanos Kourtis |

Preprint link: | scipost_201908_00005v1 |

Date submitted: | 2019-08-05 |

Submitted by: | Kourtis, Stefanos |

Submitted to: | SciPost Physics |

Discipline: | Physics |

Subject area: | Condensed Matter Physics - Computational |

Approaches: | Theoretical, 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.

### Ontology / Topics

See full Ontology or Topics database.###### Current status:

### Submission & Refereeing History

## Reports on this Submission

### Anonymous Report 2 on 2019-10-17 Invited Report

- Cite as: Anonymous, Report on arXiv:scipost_201908_00005v1, delivered 2019-10-17, doi: 10.21468/SciPost.Report.1238

### Strengths

1- The paper is well-organized and well-written.

2- The paper is perfectly understandable for the tensor-network expert who is not familiar with CSPs, and (I assume) the other way around.

3- The benchmarks or "numerical experiments" are sound and the comparison with other state-of-the-art methods is convincing.

### Weaknesses

none

### Report

It would be good to clearly mention somewhere to what extent the two test cases are favourable to the tensor-network algorithms as compared to other techniques. The speed-ups that the authors found for these two cases, are these expected to be generic for a broad class of problems?

### Requested changes

none

### 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.