Hardware-Aware QUBO Reformulation of Constrained Binary Optimization via the Walsh-Fourier Transform

Quantum Physics arXiv:2607.26349 (quant-ph) [Submitted on 28 Jul 2026] Title:Hardware-Aware QUBO Reformulation of Constrained Binary Optimization via the Walsh-Fourier Transform Authors:Loong Kuan Lee, Harsha Nagarajan, Thore Gerlach, Sascha Mücke, Ragavi Krishnamoorthy, Nico Piatkowski View a PDF of the paper titled Hardware-Aware QUBO Reformulation of Constrained Binary Optimization via the Walsh-Fourier Transform, by Loong Kuan Lee and 5 other authors View PDF HTML (experimental) Abstract:We present a novel slack-free, penalty-based framework for reformulating constrained binary optimization as Quadratic Unconstrained Binary Optimization (QUBO) on near-term quantum annealing hardware. Given a user-chosen penalty function that most naturally captures a constraint---typically non-quadratic, such as a Heaviside-function surrogate---and a target probability measure over the Boolean hypercube, our method returns the weighted least-squares projection of the chosen penalty function onto the subspace spanned by linear and quadratic Walsh--Fourier characters that correspond to physically realizable couplings on the target hardware graph. Within this restricted family, the resulting quadratic surrogate is uniquely and optimally determined by the normal equations: unlike state-of-the-art approaches, it introduces no per-constraint penalty coefficients to tune and avoids dense all-pairs couplings by construction. Two practical consequences follow. First, the projected penalty respects device connectivity, reducing chain lengths and physical-qubit overhead after minor embedding. Second, we show empirically that this hardware-native surrogate can outperform denser full-pairwise projections, despite being drawn from a strictly smaller approximation space. This advantage widens once the QUBO is embedded and sampled on quantum annealers, yielding samples with the lowest worst-case and mean objective gaps compared to unbalanced penalization and a hardware-blind projection onto all quadratic terms. Comments: Subjects: Quantum Physics (quant-ph); Optimization and Control (math.OC) Report number: LA-UR-26-24049 Cite as: arXiv:2607.26349 [quant-ph] (or arXiv:2607.26349v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.26349 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Loong Kuan Lee [view email] [v1] Tue, 28 Jul 2026 23:45:18 UTC (1,016 KB) Full-text links: Access Paper: View a PDF of the paper titled Hardware-Aware QUBO Reformulation of Constrained Binary Optimization via the Walsh-Fourier Transform, by Loong Kuan Lee and 5 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-07 Change to browse by: math math.OC References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)