An edge-based and subspace reduction encoding scheme to solve the traveling salesman problem in quantum computers

TL;DR

This paper proposes a new edge-based encoding scheme combined with subspace reduction to efficiently solve small TSP instances on quantum computers, demonstrating improved resource utilization and solution quality.

Contribution

It introduces a novel edge-based encoding and subspace reduction method for TSP on quantum computers, outperforming traditional node-based encodings in resource efficiency.

Findings

Successfully solved 4-, 5-, 6-city TSP instances on quantum hardware.

Proposed encoding outperforms conventional methods in resource use and efficiency.

Achieved optimal solutions for small TSP instances on real quantum devices.

Abstract

This paper introduces a novel edge-based encoding technique for solving the Traveling Salesman Problem (TSP) on a quantum computer, reducing the required number of qubits. For implementation in real quantum devices, we applied the subspace reduction encoding to further reduce the dimension of the TSP solution space. We attack the TSP for 4-, 5-, and 6-city instances in both simulators and real quantum computers across different encoding frameworks. Optimal solutions of the 4-city TSP instance are obtained on state-of-the art IQM quantum computer. Our study presents a comparative analysis between edge-based encoding scheme and the node-based encoding methodology in the literature. Our findings indicate that the proposed encoding scheme outperforms conventional methods in terms of statistical measures, quantum resource utilization, and computational efficiency when applied to smaller TSP instances.