Sampled-Based Guided Quantum Walk: Non-variational quantum algorithm for combinatorial optimization
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| Title: | Sampled-Based Guided Quantum Walk: Non-variational quantum algorithm for combinatorial optimization |
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| Authors: | Nzongani, Ugo, Mermoud, Dylan Laplace, Di Molfetta, Giuseppe, Simonetto, Andrea |
| Contributors: | Laboratoire d'Informatique et des Systèmes (LIS) (Marseille, Toulon) (LIS), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), Optimisation et commande (OC), Unité de Mathématiques Appliquées (UMA), École Nationale Supérieure de Techniques Avancées (ENSTA), Institut Polytechnique de Paris (IP Paris)-Institut Polytechnique de Paris (IP Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA), Institut Polytechnique de Paris (IP Paris)-Institut Polytechnique de Paris (IP Paris), ANR-22-PNCQ-0002,HQI – R&D et Support,Initiative Nationale Hybride HPC Quantique – R&D et Support des communautés(2022), ANR-22-PETQ-0007,EPiQ,Etude de la pile quantique : Algorithmes, modèles de calcul et simulation pour l'informatique quantique(2022), ANR-22-CE47-0002,DisQC,Calcul Quantique Distribué : Algorithmes et Implémentations(2022) |
| Source: | https://hal.science/hal-05280866 ; 2025. |
| Publisher Information: | CCSD |
| Publication Year: | 2025 |
| Subject Terms: | Quantum Physics (quant-ph), FOS: Physical sciences, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] |
| Description: | We introduce SamBa-GQW, a novel quantum algorithm for solving binary combinatorial optimization problems of arbitrary degree with no use of any classical optimizer. The algorithm is based on a continuous-time quantum walk on the solution space represented as a graph. The walker explores the solution space to find its way to vertices that minimize the cost function of the optimization problem. The key novelty of our algorithm is an offline classical sampling protocol that gives information about the spectrum of the problem Hamiltonian. Then, the extracted information is used to guide the walker to high quality solutions via a quantum walk with a time-dependent hopping rate. We investigate the performance of SamBa-GQW on several quadratic problems, namely MaxCut, maximum independent set, portfolio optimization, and higher-order polynomial problems such as LABS, MAX-$k$-SAT and a quartic reformulation of the travelling salesperson problem. We empirically demonstrate that SamBa-GQW finds high quality approximate solutions on problems up to a size of $n=20$ qubits by only sampling $n^2$ states among $2^n$ possible decisions. SamBa-GQW compares very well also to other guided quantum walks and QAOA. |
| Document Type: | report |
| Language: | English |
| Relation: | info:eu-repo/semantics/altIdentifier/arxiv/2509.15138; ARXIV: 2509.15138 |
| DOI: | 10.48550/arXiv.2509.15138 |
| Availability: | https://hal.science/hal-05280866 https://doi.org/10.48550/arXiv.2509.15138 |
| Accession Number: | edsbas.13111518 |
| Database: | BASE |
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