Programming guide for solving constraint satisfaction problems with tensor networks

TL;DR

This paper presents a comprehensive Julia-based framework for solving and analyzing constraint satisfaction problems by transforming them into tensor networks, optimizing contractions, and extracting solution properties.

Contribution

It introduces a novel approach to reduce CSPs to tensor networks and provides programming practices for their analysis within the Julia ecosystem.

Findings

Demonstrates reduction of CSPs to tensor networks

Shows how to optimize tensor network contraction orders

Extracts solution space properties through tensor contractions

Abstract

Constraint satisfaction problems (CSPs) are a class of problems that are ubiquitous in science and engineering. It features a collection of constraints specified over subsets of variables. A CSP can be solved either directly or by reducing it to other problems. This paper introduces the Julia ecosystem for solving and analyzing CSPs, focusing on the programming practices. We introduce some of the important CSPs and show how these problems are reduced to each other. We also show how to transform CSPs into tensor networks, how to optimize the tensor network contraction orders, and how to extract the solution space properties by contracting the tensor networks with generic element types. Examples are given, which include computing the entropy constant, analyzing the overlap gap property, and the reduction between CSPs.