Scalable Quantum Walk-Based Heuristics for the Minimum Vertex Cover Problem

• URL: http://arxiv.org/abs/2512.02940v1
• Date: Tue, 02 Dec 2025 17:04:57 GMT
• Title: Scalable Quantum Walk-Based Heuristics for the Minimum Vertex Cover Problem
• Authors: F. S. Luiz, A. K. F. Iwakami, D. H. Moraes, M. C. de Oliveira,
• Abstract summary: We propose a novel quantum algorithm for the Minimum Vertex Cover (MVC) problem based on continuous-time quantum walks (CTQWs)<n>In this framework, the coherent propagation of a quantum walker over a graph encodes its structural properties into state amplitudes.<n>We show that the CTQW-based algorithm consistently achieves superior approximation ratios and exhibits remarkable robustness with respect to network topology.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a novel heuristic quantum algorithm for the Minimum Vertex Cover (MVC) problem based on continuous-time quantum walks (CTQWs). In this framework, the coherent propagation of a quantum walker over a graph encodes its structural properties into state amplitudes, enabling the identification of highly influential vertices through their transition probabilities. To enhance stability and solution quality, we introduce a dynamic decoupling (``freezing'') mechanism that isolates vertices already selected for the cover, preventing their interference in subsequent iterations of the algorithm. The method employs a compact binary encoding, requiring only $\lceil \log_2 (V)\rceil$ qubits to represent a graph with $V$ vertices, resulting in an exponential reduction of quantum resources compared to conventional vertex-based encodings. We benchmark the proposed heuristic against exact solutions obtained via Mixed-Integer Linear Programming (MILP) and against established classical heuristics, including Simulated Annealing, FastVC, and the 2-Approximation algorithm, across Erdős--Rényi, Barabási--Albert and regular random graph ensembles. Our results demonstrate that the CTQW-based heuristic consistently achieves superior approximation ratios and exhibits remarkable robustness with respect to network topology, outperforming classical approaches in both heterogeneous and homogeneous structures. These findings indicate that continuous-time quantum walks, when combined with topology-independent decoupling strategies, provide a powerful paradigm for large-scale combinatorial optimization and complex network control, with potential applications spanning infrastructure resilience, epidemic containment, sensor network optimization, and biological systems analysis.

Related papers

• Exact and Asymptotically Complete Robust Verifications of Neural Networks via Quantum Optimization [9.728049285140736]
  We introduce two quantum-optimization-based models for robust verification of deep neural networks.<n>Experiments on benchmarks show high certification accuracy, indicating that quantum optimization can serve as a principled primitive for robustness guarantees.
  arXiv  Detail & Related papers  (2026-02-28T02:05:02Z)
• Improving Generalization and Trainability of Quantum Eigensolvers via Graph Neural Encoding [0.5013248430919223]
  Ground state of a many-body Hamiltonian is a central problem across physics, chemistry, and optimization.<n>We propose an end-to-end representation learning framework that combines a graph autoencoder with a classical neural network.<n>We demonstrate improved generalization and trainability, manifested as reduced test error and a significantly milder decay of gradient variance.
  arXiv  Detail & Related papers  (2026-02-23T12:01:14Z)
• Physics-Informed Hybrid Quantum-Classical Dispatching for Large-Scale Renewable Power Systems:A Noise-Resilient Framework [9.378801906395179]
  High-penetration energy introduces significantity and non-Classicality into power system dispatching optimization.<n>Existing approaches typically treat the power grid as a "black box"<n>This paper proposes a Hybrid Quantum-Bridging Dispatching (PIHQ-CD) framework.
  arXiv  Detail & Related papers  (2026-01-26T13:35:54Z)
• Continual Quantum Architecture Search with Tensor-Train Encoding: Theory and Applications to Signal Processing [68.35481158940401]
  CL-QAS is a continual quantum architecture search framework.<n>It mitigates challenges of costly encoding amplitude and forgetting in variational quantum circuits.<n>It achieves controllable robustness expressivity, sample-efficient generalization, and smooth convergence without barren plateaus.
  arXiv  Detail & Related papers  (2026-01-10T02:36:03Z)
• Quantum-Assisted Correlation Clustering [3.8448698053186843]
  This work introduces a hybrid quantum-classical method to correlation clustering, a graph-based unsupervised learning task.<n>We adapt GCS-Q, a quantum-assisted solver originally designed for coalition structure generation, to maximize intra-cluster agreement in signed graphs.<n> Empirical evaluations on synthetic signed graphs and real-world hyperspectral imaging data demonstrate that, when adapted for correlation clustering, GCS-Q outperforms classical algorithms in robustness and clustering quality.
  arXiv  Detail & Related papers  (2025-09-03T12:14:35Z)
• Sheaf Graph Neural Networks via PAC-Bayes Spectral Optimization [13.021238902084647]
  Over-smoothing in Graph Neural Networks (GNNs) causes collapse in distinct node features.<n>We introduce SGPC (Sheaf GNNs with PAC-Bayes), a unified architecture that combines cellular-sheaf message passing with several mechanisms.<n> Experiments on nine homophilic and heterophilic benchmarks show that SGPC outperforms state-of-the-art spectral and sheaf-based GNNs.
  arXiv  Detail & Related papers  (2025-08-01T06:39:28Z)
• Quantum-Classical Hybrid Quantized Neural Network [8.382617481718643]
  We present a novel Quadratic Binary Optimization (QBO) model for quantized neural network training, enabling the use of arbitrary activation and loss functions.<n>We employ the Quantum Gradient Conditional Descent (QCGD) algorithm, which leverages quantum computing to directly solve the QCBO problem.
  arXiv  Detail & Related papers  (2025-06-23T02:12:36Z)
• Solving Zero-Sum Convex Markov Games [38.68653814645517]
  We contribute the first provable guarantees of global convergence to Nash equilibria (NE) in two-player zero-sum games (cMGs) by using independent methods.<n>We address the general constrained min-max problems under NC-p and two-sided pPL conditions.
  arXiv  Detail & Related papers  (2025-06-19T08:12:02Z)
• Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking [45.147301546565316]
  This paper considers the problem of decentralized optimization on compact submanifolds.<n>We propose an algorithm where agents update variables using quantized variables.<n>To the best of our knowledge, this is the first algorithm to achieve an $mathcalO (1/K)$ convergence rate in the presence of quantization.
  arXiv  Detail & Related papers  (2025-06-09T01:57:25Z)
• Branch-and-bound digitized counterdiabatic quantum optimization [39.58317527488534]
  Branch-and-bound algorithms effectively solve convex optimization problems, relying on the relaxation the objective function to obtain tight lower bounds.<n>We propose a branch-and-bound digitized counterdiabatic quantum optimization (BB-DCQO) algorithm that addresses the relaxation difficulties.
  arXiv  Detail & Related papers  (2025-04-21T18:19:19Z)
• QAMA: Scalable Quantum Annealing Multi-Head Attention Operator for Deep Learning [48.12231190677108]
  Quantum Annealing Multi-Head Attention (QAMA) is proposed, a novel drop-in operator that reformulates attention as an energy-based Hamiltonian optimization problem.<n>In this framework, token interactions are encoded into binary quadratic terms, and quantum annealing is employed to search for low-energy configurations.<n> Empirically, evaluation on both natural language and vision benchmarks shows that, across tasks, accuracy deviates by at most 2.7 points from standard multi-head attention.
  arXiv  Detail & Related papers  (2025-04-15T11:29:09Z)
• A Quantum Genetic Algorithm Framework for the MaxCut Problem [49.59986385400411]
  The proposed method introduces a Quantum Genetic Algorithm (QGA) using a Grover-based evolutionary framework and divide-and-conquer principles.<n>On complete graphs, the proposed method consistently achieves the true optimal MaxCut values, outperforming the Semidefinite Programming (SDP) approach.<n>On ErdHos-R'enyi random graphs, the QGA demonstrates competitive performance, achieving median solutions within 92-96% of the SDP results.
  arXiv  Detail & Related papers  (2025-01-02T05:06:16Z)
• Bias-field digitized counterdiabatic quantum optimization [39.58317527488534]
  We call this protocol bias-field digitizeddiabatic quantum optimization (BF-DCQO) Our purely quantum approach eliminates the dependency on classical variational quantum algorithms. It achieves scaling improvements in ground state success probabilities, increasing by up to two orders of magnitude.
  arXiv  Detail & Related papers  (2024-05-22T18:11:42Z)

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.