Graph-Structured Number-Conserving Variational Quantum Eigensolver for Fermionic Pairing Hamiltonians

[2604.00844] Graph-Structured Number-Conserving Variational Quantum Eigensolver for Fermionic Pairing Hamiltonians Skip to main content Search Submit Donate Log in Quantum Physics arXiv:2604.00844 (quant-ph) [Submitted on 1 Apr 2026 ( v1 ), last revised 26 Aug 2026 (this version, v2)] Title: Graph-Structured Number-Conserving Variational Quantum Eigensolver for Fermionic Pairing Hamiltonians Authors: Abhishek , Nabeel Salim , P. Arumugam View PDF HTML (experimental) Abstract: Simulating strongly correlated fermionic pairing in the presence of rotational and pair-breaking fields requires deep quantum circuits. We present a graph-structured variational quantum eigensolver whose pair-transfer and single-excitation rotations follow the nonzero pairing and one-body mixing edges of the Hamiltonian. The circuit conserves particle number exactly and uses one parameter per retained edge. We benchmark one layer against exact fixed-number diagonalization for 1500, $M=8$ Hamiltonians represented by 16 qubits. Its mean energy error rises from 0.86 keV without one-body driving to 691 keV at the strongest drive; the one-layer circuit loses accuracy as pair breaking strengthens. In a matched eight-qubit comparison, the graph circuit reaches the 0.42 keV high-drive error of a pair-plus-all-singles circuit with 8 instead of 34 parameters. Fixed-number Adaptive Derivative-Assembled Pseudo-Trotter VQE reaches 0.056 keV with 304 decomposed controlled-NOT gates and iterative pool screening, while a 52-parameter, single-repetition unitary coupled-cluster singles-and-doubles circuit gives 17.6 keV with 2752 such gates. At a separate twelve-qubit point, a second graph layer reduces the high-drive error from 378 to 35 keV. Across the exact grid, an off-diagonal pair-coherence scale tracks the leading pair-density eigenvalue, condensate fraction, and interaction energy. Cranked zirconium Hamiltonians provide the benchmark instances and tune the strength of one-body pair breaking. Comments: 12 pages, 8 figures Subjects: Quantum Physics (quant-ph) ; Nuclear Theory (nucl-th) Cite as: arXiv:2604.00844 [quant-ph] (or arXiv:2604.00844v2 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.00844 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Abhishek Abhishek [ view email ] [v1] Wed, 1 Apr 2026 12:54:29 UTC (108 KB) [v2] Wed, 26 Aug 2026 18:40:02 UTC (322 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2026-04 Change to browse by: nucl-th 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. 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? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from (opens in new tab) (opens in new tab) (opens in new tab)

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