- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Applied

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Sparse-graph optimization using weighted quantum wires in Rydberg-atom arrays

A. G. de Oliveira1,*, J. Kombe1, G. Pelegrí1, P. Schroff1, M. T. Wells-Pestell1, D. M. Walker1, A. J. Daley1,2, and J. D. Pritchard1,†

  • *Contact author: andre.oliveira@strath.ac.uk
  • †Contact author: jonathan.pritchard@strath.ac.uk
PDF

Phys. Rev. Applied 26, 024007 – Published 5 August, 2026

DOI: https://doi.org/10.1103/bxsl-f1zc

Abstract

Neutral atom arrays provide a versatile platform to implement coherent quantum annealing as an approach to solving hard combinatorial optimization problems. Here we present and experimentally demonstrate an efficient encoding scheme based on chains of Rydberg-blockaded atoms, which we call quantum wires, to natively embed maximum weighted independent set (MWIS) and quadratic unconstrained binary optimization (QUBO) problems on a neutral atom architecture. For graphs with quasi-unit-disk connectivity, in which only a few long-range edges are required, our approach requires a significantly lower overhead in the number of ancilla qubits than previous proposals, facilitating the implementation on currently available hardware. To demonstrate the approach, we perform annealing of weighted graphs on a programmable atom array using local light shifts to encode problem-specific weights across graphs of varying sizes. This approach successfully identifies the solutions to the original MWIS and QUBO graph instances. Our work expands the operational toolkit of near-term neutral atom arrays, enhancing their potential for scalable quantum optimization.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (47)

  1. V. T. Paschos, Applications of Combinatorial Optimization (John Wiley & Sons, New York, 2014), Vol. 3.
  2. A. Abbas et al., Challenges and opportunities in quantum optimization, Nat. Rev. Phys. 6, 718 (2024).
  3. P. Hauke, H. G. Katzgraber, W. Lechner, H. Nishimori, and W. D. Oliver, Perspectives of quantum annealing: Methods and implementations, Rep. Progress Phys. 83, 054401 (2020).
  4. A. Rajak, S. Suzuki, A. Dutta, and B. K. Chakrabarti, Quantum annealing: An overview, Philos. Trans. R. Soc. A 381, 20210417 (2023).
  5. M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincio, and P. J. Coles, Variational quantum algorithms, Nat. Rev. Phys. 3, 625 (2021).
  6. N. Astrakhantsev, G. Mazzola, I. Tavernelli, and G. Carleo, Phenomenological theory of variational quantum ground-state preparation, Phys. Rev. Res. 5, 033225 (2023).
  7. A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O’Brien, A variational eigenvalue solver on a photonic quantum processor, Nat. Commun. 5, 4213 (2014).
  8. A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta, Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets, Nature (London) 549, 242 (2017).
  9. C. Hempel, C. Maier, J. Romero, J. McClean, T. Monz, H. Shen, P. Jurcevic, B. P. Lanyon, P. Love, R. Babbush, A. Aspuru-Guzik, R. Blatt, and C. F. Roos, Quantum chemistry calculations on a trapped-ion quantum simulator, Phys. Rev. X 8, 031022 (2018).
  10. C. Kokail, C. Maier, R. van Bijnen, T. Brydges, M. K. Joshi, P. Jurcevic, C. A. Muschik, P. Silvi, R. Blatt, C. F. Roos, and P. Zoller, Self-verifying variational quantum simulation of lattice models, Nature (London) 569, 355 (2019).
  11. A. Lucas, Ising formulations of many np problems, Front. Phys. 2, 5 (2014).
  12. L. Henriet, L. Beguin, A. Signoles, T. Lahaye, A. Browaeys, G.-O. Reymond, and C. Jurczak, Quantum computing with neutral atoms, Quantum 4, 327 (2020).
  13. M. Morgado and S. Whitlock, Quantum simulation and computing with rydberg-interacting qubits, AVS Quantum Sci. 3, 023501 (2021).
  14. H. Pichler, S.-T. Wang, L. Zhou, S. Choi, and M. D. Lukin, Quantum optimization for maximum independent set using Rydberg atom arrays, arXiv:1808.10816.
  15. H. Pichler, S.-T. Wang, L. Zhou, S. Choi, and M. D. Lukin, Computational complexity of the Rydberg blockade in two dimensions, arXiv:1809.04954.
  16. S. Ebadi et al., Quantum optimization of maximum independent set using Rydberg atom arrays, Science 376, 1209 (2022).
  17. K. Kim, M. Kim, J. Park, A. Byun, and J. Ahn, Quantum computing dataset of maximum independent set problem on king lattice of over hundred Rydberg atoms, Sci. Data 11, 111 (2024).
  18. R. S. Andrist, M. J. A. Schuetz, P. Minssen, R. Yalovetzky, S. Chakrabarti, D. Herman, N. Kumar, G. Salton, R. Shaydulin, Y. Sun, M. Pistoia, and H. G. Katzgraber, Hardness of the maximum-independent-set problem on unit-disk graphs and prospects for quantum speedups, Phys. Rev. Res. 5, 043277 (2023).
  19. M. Kim, K. Kim, J. Hwang, E.-G. Moon, and J. Ahn, Rydberg quantum wires for maximum independent set problems, Nat. Phys. 18, 755 (2022).
  20. A. Byun, M. Kim, and J. Ahn, Finding the maximum independent sets of platonic graphs using rydberg atoms, PRX Quantum 3, 030305 (2022).
  21. C. Dalyac, L.-P. Henry, M. Kim, J. Ahn, and L. Henriet, Exploring the impact of graph locality for the resolution of mis with neutral atom devices, arXiv:2306.13373.
  22. A. Byun, J. Jung, K. Kim, M. Kim, S. Jeong, H. Jeong, and J. Ahn, Rydberg-atom graphs for quadratic unconstrained binary optimization problems, Adv. Quantum Technol. 7, 2300398 (2024).
  23. A. Byun, S. Jeong, and J. Ahn, Programming higher-order interactions of rydberg atoms, Phys. Rev. A 110, 042612 (2024).
  24. S. Jeong, M. Kim, M. Hhan, J. Y. Park, and J. Ahn, Quantum programming of the satisfiability problem with rydberg atom graphs, Phys. Rev. Res. 5, 043037 (2023).
  25. M. Lanthaler, K. Ender, C. Dlaska, and W. Lechner, Quantum optimization with globally driven neutral atom arrays, arXiv:2410.03902.
  26. K. Goswami, R. Mukherjee, H. Ott, and P. Schmelcher, Solving optimization problems with local light-shift encoding on Rydberg quantum annealers, Phys. Rev. Res. 6, 023031 (2024).
  27. A. G. de Oliveira, E. Diamond-Hitchcock, D. M. Walker, M. T. Wells-Pestell, G. Pelegrí, C. J. Picken, G. P. A. Malcolm, A. J. Daley, J. Bass, and J. D. Pritchard, Demonstration of weighted-graph optimization on a rydberg-atom array using local light shifts, PRX Quantum 6, 010301 (2025).
  28. M.-T. Nguyen, J.-G. Liu, J. Wurtz, M. D. Lukin, S.-T. Wang, and H. Pichler, Quantum optimization with arbitrary connectivity using Rydberg atom arrays, PRX Quantum 4, 010316 (2023).
  29. L. Bombieri, Z. Zeng, R. Tricarico, R. Lin, S. Notarnicola, M. Cain, M. D. Lukin, and H. Pichler, Quantum adiabatic optimization with Rydberg arrays: Localization phenomena and encoding strategies, PRX Quantum 6, 020306 (2025).
  30. W. Lechner, P. Hauke, and P. Zoller, A quantum annealing architecture with all-to-all connectivity from local interactions, Sci. Adv. 1, e1500838 (2015).
  31. M. Lanthaler, C. Dlaska, K. Ender, and W. Lechner, Rydberg-blockade-based parity quantum optimization, Phys. Rev. Lett. 130, 220601 (2023).
  32. J. Park, S. Jeong, M. Kim, K. Kim, A. Byun, L. Vignoli, L.-P. Henry, L. Henriet, and J. Ahn, Rydberg-atom experiment for the integer factorization problem, Phys. Rev. Res. 6, 023241 (2024).
  33. M. J. A. Schuetz, R. S. Andrist, G. Salton, R. Yalovetzky, R. Raymond, Y. Sun, A. Acharya, S. Chakrabarti, M. Pistoia, and H. G. Katzgraber, Quantum compilation toolkit for Rydberg atom arrays with implications for problem hardness and quantum speedups, Phys. Rev. Res. 7, 033107 (2025).
  34. X. Qiu, P. Zoller, and X. Li, Programmable quantum annealing architectures with ising quantum wires, PRX Quantum 1, 020311 (2020).
  35. G. Kochenberger, J.-K. Hao, F. Glover, M. Lewis, Z. Lü, H. Wang, and Y. Wang, The unconstrained binary quadratic programming problem: A survey, J. Comb. Optimiz. 28, 58 (2014).
  36. QuEra Computing, UnitDiskMapping.jl (2025), https://github.com/QuEraComputing/UnitDiskMapping.jl.
  37. M. J. A. Schuetz, R. Yalovetzky, R. S. Andrist, G. Salton, Y. Sun, R. Raymond, S. Chakrabarti, A. Acharya, R. Shaydulin, M. Pistoia, and H. G. Katzgraber, qReduMIS: A quantum-informed reduction algorithm for the maximum independent set problem, arXiv:2503.12551.
  38. T. Koch et al., Quantum optimization benchmarking library—The intractable decathlon, arXiv:2504.03832.
  39. A. Oliveira, J. Kombe, G. Pelegri, P. Schroff, M. Wells-Pestell, D. Walker, A. Daley, and J. Pritchard, Data for “Sparse Graph Optimization using Weighted Quantum Wires in Rydberg Atom Arrays”, 10.15129/e3899a58-be72-4ed8-b033-32c52b1414e7 (2026).
  40. S. R. White, Density matrix formulation for quantum renormalization groups, Phys. Rev. Lett. 69, 2863 (1992).
  41. S. R. White, Density-matrix algorithms for quantum renormalization groups, Phys. Rev. B 48, 10345 (1993).
  42. U. Schollwöck, The density-matrix renormalization group in the age of matrix product states, Ann. Phys. (Amsterdam) 326, 96 (2011).
  43. M. Fishman, S. R. White, and E. M. Stoudenmire, The ITensor software library for tensor network calculations, SciPost Phys. Codebases 4 (2022).
  44. M. Fishman, S. R. White, and E. M. Stoudenmire, Codebase release 0.3 for ITensor, SciPost Phys. Codebases 4 (2022).
  45. P. Schroff, A. La Rooij, E. Haller, and S. Kuhr, Accurate holographic light potentials using pixel crosstalk modelling, Sci. Rep. 13, 3252 (2023).
  46. N. Sibalić, J. D. Pritchard, C. S. Adams, and K. J. Weatherill, ARC: An open-source library for calculating properties of alkali Rydberg atoms, Comp. Phys. Comm. 220, 319 (2017).
  47. D. Kim, A. Keesling, A. Omran, H. Levine, H. Bernien, M. Greiner, M. D. Lukin, and D. R. Englund, Large-scale uniform optical focus array generation with a phase spatial light modulator, Opt. Lett. 44, 3178 (2019).

Outline

Information

Phys. Rev. Applied 26, 024007– Published 5 August, 2026
  • Received 20 November 2025
  • Revised 27 April 2026
  • Accepted 6 July 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation