Hybrid Quantum-Classical Optimisation of Traveling Salesperson Problem

• URL: http://arxiv.org/abs/2503.00219v1
• Date: Fri, 28 Feb 2025 22:07:28 GMT
• Title: Hybrid Quantum-Classical Optimisation of Traveling Salesperson Problem
• Authors: Christos Lytrosyngounis, Ioannis Lytrosyngounis,
• Abstract summary: The Traveling Salesperson Problem (TSP) is a fundamental NP-hard optimisation challenge.<n>We present a hybrid quantum-classical approach that integrates quantum optimisation techniques with classical machine learning methods.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Traveling Salesperson Problem (TSP) is a fundamental NP-hard optimisation challenge with widespread applications in logistics, operations research, and network design. While classical algorithms effectively solve small to medium-sized instances, they struggle with scalability due to exponential complexity. In this work, we present a hybrid quantum-classical approach that leverages IBM's Qiskit Runtime to integrate quantum optimisation techniques with classical machine learning methods, specifically K-Means clustering and Random Forest classifiers. These machine learning components aid in problem decomposition and noise mitigation, improving the quality of quantum solutions. Experimental results for TSP instances ranging from 4 to 8 cities reveal that the quantum-only approach produces solutions up to 21.7% worse than the classical baseline, while the hybrid method reduces this cost increase to 11.3% for 8 cities. This demonstrates that hybrid approaches improve solution quality compared to purely quantum methods but remain suboptimal compared to classical solvers. Despite current hardware limitations, these results highlight the potential of quantum-enhanced methods for combinatorial optimisation, paving the way for future advancements in scalable quantum computing frameworks.

Related papers

• A Comparative Study of Quantum Optimization Techniques for Solving Combinatorial Optimization Benchmark Problems [4.266376725904727]
  We introduce a comprehensive benchmarking framework designed to evaluate quantum optimization techniques against well-established NP-hard problems. Our framework focuses on key problem classes, including the Multi-Dimensional Knapsack Problem (MDKP), Maximum Independent Set (MIS), Quadratic Assignment Problem (QAP), and Market Share Problem (MSP)
  arXiv  Detail & Related papers  (2025-03-15T13:02:22Z)
• Quantum Subroutines in Branch-Price-and-Cut for Vehicle Routing [0.0]
  We demonstrate in this work how quantums with limited resources can be integrated in large-scale exact optimization algorithms for NP-hard problems.<n>A key feature of our algorithm is it not only from the best solution returned by the quantum but from all solutions below a certain cost threshold.
  arXiv  Detail & Related papers  (2024-12-20T08:27:23Z)
• Bayesian Parameterized Quantum Circuit Optimization (BPQCO): A task and hardware-dependent approach [49.89480853499917]
  Variational quantum algorithms (VQA) have emerged as a promising quantum alternative for solving optimization and machine learning problems. In this paper, we experimentally demonstrate the influence of the circuit design on the performance obtained for two classification problems. We also study the degradation of the obtained circuits in the presence of noise when simulating real quantum computers.
  arXiv  Detail & Related papers  (2024-04-17T11:00:12Z)
• Solving non-native combinatorial optimization problems using hybrid quantum-classical algorithms [0.0]
  Combinatorial optimization is a challenging problem applicable in a wide range of fields from logistics to finance. Quantum computing has been used to attempt to solve these problems using a range of algorithms. This work presents a framework to overcome these challenges by integrating quantum and classical resources with a hybrid approach.
  arXiv  Detail & Related papers  (2024-03-05T17:46:04Z)
• A Quantum-Classical Collaborative Training Architecture Based on Quantum State Fidelity [50.387179833629254]
  We introduce a collaborative classical-quantum architecture called co-TenQu. Co-TenQu enhances a classical deep neural network by up to 41.72% in a fair setting. It outperforms other quantum-based methods by up to 1.9 times and achieves similar accuracy while utilizing 70.59% fewer qubits.
  arXiv  Detail & Related papers  (2024-02-23T14:09:41Z)
• Formulation of the Electric Vehicle Charging and Routing Problem for a Hybrid Quantum-Classical Search Space Reduction Heuristic [0.0]
  We show how to exploit multilevel carriers of quantum information -- qudits -- for the construction of constrained quantum optimization algorithms. We propose a hybrid classical quantum strategy that allows us to sample constrained solutions while greatly reducing the search space of the problem.
  arXiv  Detail & Related papers  (2023-06-07T13:16:15Z)
• Quantum Annealing for Single Image Super-Resolution [86.69338893753886]
  We propose a quantum computing-based algorithm to solve the single image super-resolution (SISR) problem. The proposed AQC-based algorithm is demonstrated to achieve improved speed-up over a classical analog while maintaining comparable SISR accuracy.
  arXiv  Detail & Related papers  (2023-04-18T11:57:15Z)
• Synergy Between Quantum Circuits and Tensor Networks: Short-cutting the Race to Practical Quantum Advantage [43.3054117987806]
  We introduce a scalable procedure for harnessing classical computing resources to provide pre-optimized initializations for quantum circuits. We show this method significantly improves the trainability and performance of PQCs on a variety of problems. By demonstrating a means of boosting limited quantum resources using classical computers, our approach illustrates the promise of this synergy between quantum and quantum-inspired models in quantum computing.
  arXiv  Detail & Related papers  (2022-08-29T15:24:03Z)
• Adapting Quantum Approximation Optimization Algorithm (QAOA) for Unit Commitment [2.8060379263058794]
  We formulate and apply a hybrid quantum-classical algorithm to a power system optimization problem called Unit Commitment. Our algorithm extends the Quantum Approximation Optimization Algorithm (QAOA) with a classical minimizer in order to support mixed binary optimization. Our results indicate that classical solvers are effective for our simulated Unit Commitment instances with fewer than 400 power generation units.
  arXiv  Detail & Related papers  (2021-10-25T03:37:34Z)
• Variational Quantum Optimization with Multi-Basis Encodings [62.72309460291971]
  We introduce a new variational quantum algorithm that benefits from two innovations: multi-basis graph complexity and nonlinear activation functions. Our results in increased optimization performance, two increase in effective landscapes and a reduction in measurement progress.
  arXiv  Detail & Related papers  (2021-06-24T20:16:02Z)
• Space-efficient binary optimization for variational computing [68.8204255655161]
  We show that it is possible to greatly reduce the number of qubits needed for the Traveling Salesman Problem. We also propose encoding schemes which smoothly interpolate between the qubit-efficient and the circuit depth-efficient models.
  arXiv  Detail & Related papers  (2020-09-15T18:17:27Z)
• Cross Entropy Hyperparameter Optimization for Constrained Problem Hamiltonians Applied to QAOA [68.11912614360878]
  Hybrid quantum-classical algorithms such as Quantum Approximate Optimization Algorithm (QAOA) are considered as one of the most encouraging approaches for taking advantage of near-term quantum computers in practical applications. Such algorithms are usually implemented in a variational form, combining a classical optimization method with a quantum machine to find good solutions to an optimization problem. In this study we apply a Cross-Entropy method to shape this landscape, which allows the classical parameter to find better parameters more easily and hence results in an improved performance.
  arXiv  Detail & Related papers  (2020-03-11T13:52:41Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.