Combinatorial optimisation via highly efficient quantum walks

TL;DR

This paper introduces a highly efficient quantum circuit for continuous time quantum walks that can potentially solve certain NP-hard combinatorial problems more effectively.

Contribution

It presents a novel quantum circuit design enabling efficient CTQWs over large combinatorial sets, enhancing quantum optimization algorithms.

Findings

Potential to solve NP-hard problems like TSP and graph partitioning.

Efficient quantum circuit implementation for large combinatorial spaces.

Improved prospects for quantum optimization algorithms.

Abstract

We present a highly efficient quantum circuit for performing continuous time quantum walks (CTQWs) over an exponentially large set of combinatorial objects, provided that the objects can be indexed efficiently. CTQWs form the core mixing operation of a generalised version of the Quantum Approximate Optimisation Algorithm, which works by `steering' the quantum amplitude into high-quality solutions. The efficient quantum circuit holds the promise of finding high-quality solutions to certain classes of NP-hard combinatorial problems such as the Travelling Salesman Problem, maximum set splitting, graph partitioning, and lattice path optimisation.