Solving the Traveling Salesman Problem via Different Quantum Computing Architectures

TL;DR

This paper compares various emerging quantum and photonic architectures for solving the NP-hard Traveling Salesman Problem, highlighting their scalability, accuracy, and potential advantages over classical methods.

Contribution

It provides a comprehensive analysis of quantum and photonic approaches to TSP, demonstrating their scalability and performance limitations and advantages across different architectures.

Findings

Gate-based quantum computers are accurate for small TSP instances but limited by noise and scalability.

Ising-based architectures can handle larger TSP instances with better scalability.

Ising machines show significant time advantages over classical methods despite solution suboptimality.

Abstract

We study the application of emerging photonic and quantum computing architectures to solving the Traveling Salesman Problem (TSP), a well-known NP-hard optimization problem. We investigate several approaches: Simulated Annealing (SA), Quadratic Unconstrained Binary Optimization (QUBO-Ising) methods implemented on quantum annealers and Optical Coherent Ising Machines, as well as the Quantum Approximate Optimization Algorithm (QAOA) and the Quantum Phase Estimation (QPE) algorithm on gate-based quantum computers. QAOA and QPE were tested on the IBM Quantum platform. The QUBO-Ising method was explored using the D-Wave quantum annealer, which operates on superconducting Josephson junctions, and the Quantum Computing Inc (QCi) Dirac-1 entropy quantum optimization machine. Gate-based quantum computers demonstrated accurate results for small TSP instances in simulation. However, real quantum devices are hindered by noise and limited scalability. Circuit complexity grows with problem size, restricting performance to TSP instances with a maximum of 6 nodes. In contrast, Ising-based architectures show improved scalability for larger problem sizes. SQUID-based Ising machines can handle TSP instances with up to 12 nodes, while entropy computing implemented in hybrid optoelectronic components extend this capability to 18 nodes. Nevertheless, the solutions tend to be suboptimal due to hardware limitations and challenges in achieving ground state convergence as the problem size increases. Despite these limitations, Ising machines demonstrate significant time advantages over classical methods, making them a promising candidate for solving larger-scale TSPs efficiently.