Learning-Driven Annealing with Adaptive Hamiltonian Modification for Solving Large-Scale Problems on Quantum Devices

Sebastian Schulz; Dennis Willsch; Kristel Michielsen

doi:10.22331/q-2025-10-29-1898

Learning-Driven Annealing with Adaptive Hamiltonian Modification for Solving Large-Scale Problems on Quantum Devices

Sebastian Schulz¹, Dennis Willsch^1,2, and Kristel Michielsen^1,3,4

¹Jülich Supercomputing Centre, Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
²Faculty of Medical Engineering and Technomathematics, University of Applied Sciences Aachen, 52428 Jülich, Germany
³AIDAS, 52425 Jülich, Germany
⁴RWTH Aachen University, 52056 Aachen, Germany

Published:	2025-10-29, volume 9, page 1898
Editor:	Yu Tong
Eprint:	arXiv:2502.21246v2
Doi:	https://doi.org/10.22331/q-2025-10-29-1898
Citation:	Quantum 9, 1898 (2025).

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Abstract

We present Learning-Driven Annealing (LDA), a framework that links individual quantum annealing evolutions into a global solution strategy to mitigate hardware constraints such as short annealing times and integrated control errors. Unlike other iterative methods, LDA does not tune the annealing procedure (e.g. annealing time or annealing schedule), but instead learns about the problem structure to adaptively modify the problem Hamiltonian. By deforming the instantaneous energy spectrum, LDA suppresses transitions into high-energy states and focuses the evolution into low-energy regions of the Hilbert space. We demonstrate the efficacy of LDA by developing a hybrid quantum-classical solver for large-scale spin glasses. The hybrid solver is based on a comprehensive study of the internal structure of spin glasses, outperforming other quantum and classical algorithms (e.g., reverse annealing, cyclic annealing, simulated annealing, Gurobi, Toshiba's SBM, VeloxQ and D-Wave hybrid) on 5580-qubit problem instances in both runtime and lowest energy. LDA is a step towards practical quantum computation that enables today's quantum devices to compete with classical solvers.

Featured image: Performance comparison of Learning-Driven Annealing (LDA) with quantum and classical solvers on 5580-qubit NAT-7 spin-glass instances. The figure shows the energy gap to the best-known solution as a function of wall-clock runtime. Quantum algorithms were executed on the D-Wave Advantage 5.4 system, while classical solvers were run on the JUWELS Booster supercomputer at the Jülich Supercomputing Centre.

Popular summary

We introduce Learning-Driven Annealing (LDA), an iterative framework that extends quantum annealing by adaptively modifying the problem Hamiltonian based on information extracted from previously sampled quantum states. By continuously deforming the instantaneous energy spectrum, LDA suppresses critical phase transitions and guides the system through otherwise non-adiabatic regions. This approach mitigates hardware constraints such as limited coherence times, enabling successful quantum optimization on NISQ devices.

We demonstrate the efficacy of LDA on the D-Wave Advantage 5.4 system using 5,580-qubit spin-glass instances. Across all benchmarks, LDA consistently outperforms established quantum and classical solvers (including reverse and cyclic annealing, simulated annealing, Gurobi, Toshiba’s SBM, VeloxQ, and D-Wave’s hybrid solver) in both runtime and lowest energy.

► BibTeX data

@article{Schulz2025learningdriven,
  doi = {10.22331/q-2025-10-29-1898},
  url = {https://doi.org/10.22331/q-2025-10-29-1898},
  title = {Learning-{D}riven {A}nnealing with {A}daptive {H}amiltonian {M}odification for {S}olving {L}arge-{S}cale {P}roblems on {Q}uantum {D}evices},
  author = {Schulz, Sebastian and Willsch, Dennis and Michielsen, Kristel},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1898},
  month = oct,
  year = {2025}
}

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[2] J. Tuziemski, J. Pawłowski, P. Tarasiuk, Ł. Pawela, and B. Gardas, "Limits of quantum run-time advantage", Physical Review Applied 25 4, 044084 (2026).

[3] Tomasz Śmierzchalski, Anna M. Dziubyna, Konrad Jałowiecki, Zakaria Mzaouali, Łukasz Pawela, Bartłomiej Gardas, and Marek M. Rams, "SpinGlassPEPS.jl: Tensor-network package for Ising-like optimization on quasi-two-dimensional graphs", SoftwareX 31, 102257 (2025).

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