# Solving the Traveling Salesman Problem via Different Quantum Computing Architectures

arXiv: https://arxiv.org/abs/2502.17725 · HTML: https://mlsanity.com/paper/2502.17725/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 33 references that are in the map.
- First posted on arXiv 24 Feb 2025.

## Builds on (most cited first, 3 of 3)

- [QUBO Formulations for Training Machine Learning Models](https://mlsanity.com/paper/2008.02369/) (2020)
- [Adiabatic Quantum Linear Regression](https://mlsanity.com/paper/2008.02355/) (2020)
- [Reachability Deficits in Quantum Approximate Optimization](https://mlsanity.com/paper/1906.11259/) (2019)

## Built on by (most cited first, 1 of 1)

- [Freeze and Conquer: Reusable Ansatz for Solving the Traveling Salesman Problem](https://mlsanity.com/paper/2508.21730/) (2025)

## Abstract (arXiv)

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.