Mitigating Precision Errors in Quantum Annealing via Coefficient Reduction of Embedded Hamiltonians

Quantum Physics [Submitted on 4 Apr 2026] Mitigating Precision Errors in Quantum Annealing via Coefficient Reduction of Embedded Hamiltonians Kentaro Ohno, Nozomu Togawa Quantum annealing is a quantum algorithm to solve combinatorial optimization problems. In the current quantum annealing devices, the dynamic range of the input Ising Hamiltonian, defined as the ratio of the largest to the smallest coefficient, significantly affects the quality of the output solution due to limited hardware precision. Several methods have been proposed to reduce the dynamic range by reducing large coefficients in the Ising Hamiltonian. However, existing studies do not take into account minor-embedding, which is an essential process in current quantum annealers. In this study, we revisit three existing coefficient-reduction methods under the constraints of minor-embedding. We evaluate to what extent these methods reduce the dynamic range of the minor-embedded Hamiltonian and improve the sample quality obtained from the D-Wave Advantage quantum annealer. The results show that, on the set of problems tested in this study, the interaction-extension method effectively improves the sample quality by reducing the dynamic range, while the bounded-coefficient integer encoding and the augmented Lagrangian method have only limited effects. Furthermore, we empirically show that reducing external field coefficients at the logical Hamiltonian level is not required in practice, since minor-embedding automatically has the role of reducing them. These findings suggest future directions for enhancing the sample quality of quantum annealers by suppressing hardware errors through preprocessing of the input problem. Comments: 21 pages, accepted to IEEE Transactions on Quantum Engineering Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.03546 [quant-ph]   (or arXiv:2604.03546v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.03546 Focus to learn more Related DOI: https://doi.org/10.1109/TQE.2026.3678999 Focus to learn more Submission history From: Kentaro Ohno [view email] [v1] Sat, 4 Apr 2026 02:13:50 UTC (809 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)