A Gauss-Newton based Quantum Algorithm for Combinatorial Optimization

TL;DR

This paper introduces a Gauss-Newton based quantum algorithm that efficiently solves combinatorial optimization problems by avoiding local minima and plateaus, outperforming existing methods in convergence and accuracy.

Contribution

The paper proposes a novel Gauss-Newton based quantum algorithm utilizing tensor product states for improved combinatorial optimization, addressing limitations of variational quantum algorithms.

Findings

GNQA converges rapidly to optimal solutions

Outperforms other quantum optimization methods in accuracy

Effective for various combinatorial problems

Abstract

In this work, we present a Gauss-Newton based quantum algorithm (GNQA) for combinatorial optimization problems that, under optimal conditions, rapidly converges towards one of the optimal solutions without being trapped in local minima or plateaus. Quantum optimization algorithms have been explored for decades, but more recent investigations have been on variational quantum algorithms, which often suffer from the aforementioned problems. Our approach mitigates those by employing a tensor product state that accurately represents the optimal solution, and an appropriate function for the Hamiltonian, containing all the combinations of binary variables. Numerical experiments presented here demonstrate the effectiveness of our approach, and they show that GNQA outperforms other optimization methods in both convergence properties and accuracy for all problems considered here. Finally, we briefly discuss the potential impact of the approach to other problems, including those in quantum chemistry and higher order binary optimization.