Computing solution space properties of combinatorial optimization problems via generic tensor networks

TL;DR

This paper presents a unified tensor network framework to analyze solution space properties of combinatorial optimization problems, enabling efficient computation of solutions, counting, and sampling, with applications to various models and algorithms.

Contribution

It introduces a novel, versatile tensor network approach that unifies the computation of solution space properties across different combinatorial problems.

Findings

Successfully computed entropy constants for hardcore lattice gases

Analyzed overlap gap properties in solution spaces

Assessed algorithm performance for maximum independent sets

Abstract

We introduce a unified framework to compute the solution space properties of a broad class of combinatorial optimization problems. These properties include finding one of the optimum solutions, counting the number of solutions of a given size, and enumeration and sampling of solutions of a given size. Using the independent set problem as an example, we show how all these solution space properties can be computed in the unified approach of generic tensor networks. We demonstrate the versatility of this computational tool by applying it to several examples, including computing the entropy constant for hardcore lattice gases, studying the overlap gap properties, and analyzing the performance of quantum and classical algorithms for finding maximum independent sets.