Rapid quantum approaches for combinatorial optimisation inspired by optimal state-transfer

TL;DR

This paper introduces a rapid quantum heuristic inspired by optimal state-transfer Hamiltonians, offering improved approximation ratios over QAOA at low depth for combinatorial optimization problems.

Contribution

The paper presents a novel quantum heuristic based on Hamiltonians for optimal state-transfer, demonstrating better performance than QAOA at minimal depth.

Findings

Outperforms QAOA in approximation ratio at low depth

Requires comparable quantum resources to existing algorithms

Provides a new direction for quantum combinatorial optimization

Abstract

We propose a new design heuristic to tackle combinatorial optimisation problems, inspired by Hamiltonians for optimal state-transfer. The result is a rapid approximate optimisation algorithm. We provide numerical evidence of the success of this new design heuristic. We find this approach results in a better approximation ratio than the Quantum Approximate Optimisation Algorithm at lowest depth for the majority of problem instances considered, while utilising comparable resources. This opens the door to investigating new approaches for tackling combinatorial optimisation problems, distinct from adiabatic-influenced approaches.