Multivariate quantum state preparation with optimized tensor networks

Quantum Physics arXiv:2609.09304 (quant-ph) [Submitted on 8 Sep 2026] Title:Multivariate quantum state preparation with optimized tensor networks Authors:Matthew L. Sims-Goh, Lukasz Cincio, Annina Z. Lieberherr, Mekena McGrew, Thomas R. Bromley View a PDF of the paper titled Multivariate quantum state preparation with optimized tensor networks, by Matthew L. Sims-Goh and 4 other authors View PDF Abstract:Quantics tensor trains are attracting intense interest for quantum-inspired computing and quantum state preparation. These methods, which approximate continuum functions by representing their amplitude encoding as a matrix product state (MPS), are exceedingly powerful for univariate functions but rapidly become challenging when handling multivariate functions, since the linear chain topology leads to a large distance between highly-entangled qubits. We overcome this limitation by introducing SCENT (Spectral Clustering for Entanglement miNimizing Trees). SCENT is a protocol that utilizes efficiently-computable pairwise entanglement metrics to determine a suitable tree tensor network (TTN) structure, which can then be efficiently approximated using tensor cross-interpolation (TCI); we find that it substantially outperforms MPS methods and improves upon previous TTN methods. We then apply these optimized TTNs to state preparation, introducing an approximate circuit compilation method based on environment-tensor methods without significantly conceding overall accuracy. Importantly, the inherent gauge freedom of TTNs can be directly exploited in this method, resulting in higher fidelity at a given circuit depth. We demonstrate this quantum state-preparation pipeline on archetypal state-preparation problems in quantum chemistry and financial portfolio optimization. In our flagship demonstration, we encode a 20-variable probability distribution with long-ranged, non-nearest neighbor inter-variable correlations in a 200-qubit state-preparation circuit with infidelity $7.44\times 10^{-9}$ using only 43284 CNOTs; depth and fidelity can be traded, allowing the same distribution to be prepared to infidelity $10^{-3}$ with as few as 5584 CNOTs. Comments: Subjects: Quantum Physics (quant-ph) Report number: LA-UR-26-27598 Cite as: arXiv:2609.09304 [quant-ph] (or arXiv:2609.09304v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.09304 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Matthew Sims-Goh [view email] [v1] Tue, 8 Sep 2026 18:01:11 UTC (1,269 KB) Full-text links: Access Paper: View a PDF of the paper titled Multivariate quantum state preparation with optimized tensor networks, by Matthew L. Sims-Goh and 4 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-09 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?)