Decoder-Consistent Hamiltonians for POVM-Based Quantum Relaxations

Quantum Physics [Submitted on 4 Jun 2026] Decoder-Consistent Hamiltonians for POVM-Based Quantum Relaxations Takayuki Suzuki In compression-based quantum relaxations like QRAO, classical variables are encoded into qubits and decoded after optimization. We formalize that the choice of the quantum Hamiltonian is fundamentally determined by this decoder. By representing the decoder as a POVM, we define a unique decoder-consistent Hamiltonian via the pullback of the post-decoding expected objective value. Using this framework, we reveal that standard QRAO Hamiltonians are inconsistent for certain mixed-degree quadratic functions, and we provide new approximation guarantees for the MaxCut problem based directly on POVM decoder design. Comments: Presented at AQIS 2026 Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2606.05604 [quant-ph]   (or arXiv:2606.05604v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2606.05604 Focus to learn more Submission history From: Takayuki Suzuki [view email] [v1] Thu, 4 Jun 2026 02:27:20 UTC (15 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-06 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?)