Certifying Quantum Optimization and Circuit Cutting by Using Quantum-Classical Moment Duality
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Quantum Physics arXiv:2606.23727 (quant-ph) [Submitted on 19 Jun 2026] Title:Certifying Quantum Optimization and Circuit Cutting by Using Quantum-Classical Moment Duality Authors:Ammar Daskin View a PDF of the paper titled Certifying Quantum Optimization and Circuit Cutting by Using Quantum-Classical Moment Duality, by Ammar Daskin View PDF HTML (experimental) Abstract:We establish a direct quantum-classical duality based on the degree-$2$ Sum-of-Squares (SoS) semidefinite programming cone: the matrix of two-qubit Pauli-$Z$ correlation functions obtained from \emph{any} quantum state $\rho$ is automatically a feasible point of the classical Goemans-Williamson (GW) relaxation. This observation provides a universal ``safety net'' for quantum optimization algorithms: applying GW random hyperplane rounding to the quantum-driven moment matrix yields a certified expected cut value $\mathbb{E}[\mathrm{Cut}] \ge \alpha_{\mathrm{GW}}\langle\mathcal{H}\rangle_\rho$, valid for every state produced by variational algorithms such as QAOA or the Variational Quantum Power Method (VQPM), regardless of convergence quality. We further show that the same moment matrix reveals the tensor-product structure of the underlying unitary circuit, enabling a polynomial-time, correlation-based circuit cutting procedure with rigorous error bounds. The framework is validated numerically on Max-Cut instances for variational quantum algorithms and on random states for circuit cutting, demonstrating that the cheap two-point correlation data are sufficient to locate near-optimal bipartitions and that the theoretical error bounds hold in practice. Comments: Subjects: Quantum Physics (quant-ph); Data Structures and Algorithms (cs.DS) Cite as: arXiv:2606.23727 [quant-ph] (or arXiv:2606.23727v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.23727 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ammar Daskin [view email] [v1] Fri, 19 Jun 2026 12:48:36 UTC (201 KB) Full-text links: Access Paper: View a PDF of the paper titled Certifying Quantum Optimization and Circuit Cutting by Using Quantum-Classical Moment Duality, by Ammar DaskinView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 Change to browse by: cs cs.DS 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?)