Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2512.06523 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911306197499904 |
|---|---|
| author | Goldsmith, Daniel Liang, Xing Makris, Dimitrios Wu, Hongwei |
| author_facet | Goldsmith, Daniel Liang, Xing Makris, Dimitrios Wu, Hongwei |
| contents | The Travelling Salesman Problem (TSP) is a well-known NP-Hard combinatorial optimisation problem, with industrial use cases such as last-mile delivery. Although TSP has been studied extensively on quantum computers, it is rare to find quantum solutions of TSP network with more than a dozen locations. In this paper, we present high quality solutions in noise-free Qiskit simulations of networks with up to twelve locations using a hybrid penalty-free, circuit-model, Variational Quantum Algorithm (VQA). Noisy qubits are also simulated. To our knowledge, this is the first successful VQA simulation of a twelve-location TSP on circuit-model devices. Multiple encoding strategies, including factorial, non-factorial, and Gray encoding are evaluated. Our formulation scales as $\mathcal{O}(nlog_2(n))$ qubits, requiring only 29 qubits for twelve locations, compared with over 100 qubits for conventional approaches scaling as $\mathcal{O}(n^2)$. Computational time is further reduced by almost two orders of magnitude through the use of Simultaneous Perturbation Stochastic Approximation (SPSA) gradient estimation and cost-function caching. We also introduce a novel machine-learning model, and benchmark both quantum and classical approaches against a Monte Carlo baseline. The VQA outperforms the classical machine-learning approach, and performs similarly to Monte Carlo for the small networks simulated. Additionally, the results indicate a trend toward improved performance with problem size, outlining a pathway to solving larger TSP instances on quantum devices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06523 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solving larger Travelling Salesman Problem networks with a penalty-free Variational Quantum Algorithm Goldsmith, Daniel Liang, Xing Makris, Dimitrios Wu, Hongwei Quantum Physics The Travelling Salesman Problem (TSP) is a well-known NP-Hard combinatorial optimisation problem, with industrial use cases such as last-mile delivery. Although TSP has been studied extensively on quantum computers, it is rare to find quantum solutions of TSP network with more than a dozen locations. In this paper, we present high quality solutions in noise-free Qiskit simulations of networks with up to twelve locations using a hybrid penalty-free, circuit-model, Variational Quantum Algorithm (VQA). Noisy qubits are also simulated. To our knowledge, this is the first successful VQA simulation of a twelve-location TSP on circuit-model devices. Multiple encoding strategies, including factorial, non-factorial, and Gray encoding are evaluated. Our formulation scales as $\mathcal{O}(nlog_2(n))$ qubits, requiring only 29 qubits for twelve locations, compared with over 100 qubits for conventional approaches scaling as $\mathcal{O}(n^2)$. Computational time is further reduced by almost two orders of magnitude through the use of Simultaneous Perturbation Stochastic Approximation (SPSA) gradient estimation and cost-function caching. We also introduce a novel machine-learning model, and benchmark both quantum and classical approaches against a Monte Carlo baseline. The VQA outperforms the classical machine-learning approach, and performs similarly to Monte Carlo for the small networks simulated. Additionally, the results indicate a trend toward improved performance with problem size, outlining a pathway to solving larger TSP instances on quantum devices. |
| title | Solving larger Travelling Salesman Problem networks with a penalty-free Variational Quantum Algorithm |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.06523 |