Discrete Flow-Based Generative Models for Measurement Optimization in Quantum Computing

[2509.15486] Discrete Flow-Based Generative Models for Measurement Optimization in Quantum Computing Skip to main content Search Submit Donate Log in Quantum Physics arXiv:2509.15486 (quant-ph) [Submitted on 18 Sep 2025 ( v1 ), last revised 25 Aug 2026 (this version, v3)] Title: Discrete Flow-Based Generative Models for Measurement Optimization in Quantum Computing Authors: Isaac L. Huidobro-Meezs , Jun Dai , Rodrigo A. Vargas-Hernández View PDF HTML (experimental) Abstract: Estimating molecular Hamiltonians to chemical accuracy requires a large number of measurements. Hamiltonian overlapping grouping methods focus on reducing measurement counts, employing greedy initializations, such as sorted insertion (SI), leaving useful measurement/circuit trade-offs unexplored. Here, we formulate Hamiltonian grouping as a reward-driven generative search problem and introduce a Generative Flow Networks (GFlowNets)-based model that colors graph representations of molecular qubit Hamiltonians to sample non-overlapping commuting groupings. The reward function can combine measurement cost, circuit count, and compiled two-qubit-gate count, enabling multi-objective optimization without differentiable cost functions or model pretraining. Across molecular Hamiltonian benchmarks, the GFlowNets sampler finds fully commuting non-overlapping groupings with average measurement requirements 18% lower than SI, and produces Pareto sets that expose trade-offs among shots, circuits, and two-qubit resources. When used to initialize iterative coefficient splitting (ICS), GFlowNet-generated groupings reduce post-ICS measurement estimates by up to 40% for Jordan-Wigner-mapped fully commuting Hamiltonians relative to SI initialization. Composite rewards further identify lower two-qubit gate groupings, including cases with more than 100 fewer compiled two-qubit gates, while retaining comparable post-ICS measurement benefits. GFlowNets provide a flexible workflow for resource-aware measurement and quantum-resource optimization in quantum chemistry, replacing single-heuristic outputs with diverse candidate groupings that can be selected according to hardware-specific priorities. Our results show that our GFlowNets' generative policy framework not only reduces measurement and two-qubit gate costs but also provides flexibility for hardware-aware adaptations via its reward function. Comments: 26 pages, 9 figures and 4 tables. Contact authors for SM Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2509.15486 [quant-ph] (or arXiv:2509.15486v3 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2509.15486 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1039/d6dd00430j Focus to learn more DOI(s) linking to related resources Submission history From: Isaac L. Huidobro-Meezs [ view email ] [v1] Thu, 18 Sep 2025 23:23:36 UTC (12,775 KB) [v2] Thu, 25 Jun 2026 03:17:34 UTC (19,700 KB) [v3] Tue, 25 Aug 2026 09:12:11 UTC (12,064 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2025-09 References & Citations INSPIRE HEP SciX 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 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. 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