Variational (matrix) product states for combinatorial optimization

TL;DR

This paper introduces quantum-inspired variational methods using matrix product states for combinatorial optimization, demonstrating superior performance on large maximum cut problems compared to existing algorithms.

Contribution

It presents a novel quantum-inspired variational approach combining MPS with iterated local search for large-scale combinatorial problems.

Findings

Outperforms traditional PS and MPS methods

Surpasses classical ILS and quantum approximate optimization algorithms

Effective on problems with up to 50,000 variables

Abstract

To compute approximate solutions for combinatorial optimization problems, we describe variational methods based on the product state (PS) and matrix product state (MPS) ansatzes. We perform variational energy minimization with respect to a quantum annealing Hamiltonian and utilize randomness by embedding the approaches in the metaheuristic iterated local search (ILS). The resulting quantum-inspired ILS algorithms are benchmarked on maximum cut problems of up to 50000 variables. We show that they can outperform traditional (M)PS methods, classical ILS, the quantum approximate optimization algorithm and other variational quantum-inspired solvers.