Practical Scalability of Tensor Network Quantum Emulators for Molecular Hamiltonian Simulation

[2504.11399] Practical Scalability of Tensor Network Quantum Emulators for Molecular Hamiltonian Simulation Skip to main content Search Submit Donate Log in Quantum Physics arXiv:2504.11399 (quant-ph) [Submitted on 15 Apr 2025 ( v1 ), last revised 28 Aug 2026 (this version, v2)] Title: Practical Scalability of Tensor Network Quantum Emulators for Molecular Hamiltonian Simulation Authors: Marek Kowalik , Ellen Michael , Peter Pogány , Phalgun Lolur View PDF HTML (experimental) Abstract: Quantum computing holds promise for computational chemistry, but near-term quantum hardware remains limited by noise and scale, motivating classical bridging technologies such as quantum emulators. We present an application-specific systems-level benchmark of matrix product state (MPS) tensor-network emulation for real-time Hamiltonian evolution of a density matrix embedding theory (DMET)-embedded sulfonyl-fluoride pharmaceutical fragment, using state-vector simulation as reference. We evaluate runtime, accuracy, resource requirements, and entanglement growth across active spaces from 4 to 24 qubits for a one-body temporal observable used as a quantum fingerprint for reactivity prediction. The results identify a practical boundary for this workflow. At fixed bond dimension, MPS emulation retains favorable scaling, but the bond dimension required to estimate the observable within a 1.6 mHa chemical-accuracy threshold grows rapidly with active-space size. At 20-24 qubits, it approaches the maximum available MPS representation, eliminating the runtime advantage over state-vector simulation. Entanglement entropy analysis shows that increasing bipartite entanglement in the time-evolved state drives this cost growth, consistent with a mismatch between a one-dimensional MPS ansatz and the non-local correlations generated by molecular electronic dynamics. We do not claim a universal crossover across molecules, observables, mappings, or tensor-network geometries. Rather, this study measures where MPS emulation ceases to be an efficient classical surrogate for this chemically motivated Hamiltonian-simulation workflow. The results motivate entanglement-aware algorithm design, orbital-ordering and mapping optimization, alternative tensor-network geometries, and ultimately fault-tolerant quantum hardware for regimes where accurate molecular dynamics generate non-compressible entanglement. Comments: 12 pages, 9 figures, accepted for presentation at IEEE QCE26 Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2504.11399 [quant-ph] (or arXiv:2504.11399v2 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2504.11399 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Phalgun Lolur [ view email ] [v1] Tue, 15 Apr 2025 17:14:01 UTC (896 KB) [v2] Fri, 28 Aug 2026 08:52:48 UTC (1,170 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2025-04 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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