A Block Tensor Train Burer-Monteiro Framework for Low-Rank Quantum State Tomography

Quantum Physics arXiv:2609.09457 (quant-ph) [Submitted on 8 Sep 2026] Title:A Block Tensor Train Burer-Monteiro Framework for Low-Rank Quantum State Tomography Authors:Shakir Showkat Sofi, Charlotte Vermeylen, Fatemeh Mohammadi, Lieven De Lathauwer View a PDF of the paper titled A Block Tensor Train Burer-Monteiro Framework for Low-Rank Quantum State Tomography, by Shakir Showkat Sofi and 2 other authors View PDF HTML (experimental) Abstract:Quantum state tomography is a fundamental technique for estimating the state of a quantum system from measured data and plays a crucial role in evaluating the performance of quantum devices. However, standard estimation methods become computationally prohibitive as the system size increases due to the exponential growth of the density matrix, describing a quantum state, with the number of qubits. We propose a low-rank tensor-network framework for mixed-state quantum state tomography based on a block tensor train (Block-TT) factorization. Specifically, the density matrix is represented as the contraction of a Block-TT with its Hermitian transpose, yielding a TT analogue of the Burer-Monteiro factorization. This parameterization guarantees Hermiticity and positive semidefiniteness by construction while compressing the number of optimization variables from exponential to linear in the number of qubits. Building on this representation, we develop single-site and two-site density matrix renormalization group (DMRG) algorithms for estimating quantum states from compressed measurements. The resulting methods operate directly on the compressed parameterization, support adaptive rank refinement, and exploit efficient tensor-network contractions for expectation-value evaluation. The framework is applicable to a broad class of low-rank quantum states, including pure states, nearly pure states, and ground states that admit accurate tensor-network approximations. Numerical experiments demonstrate accurate state reconstruction from limited measurements together with substantial reductions in memory requirements and computational cost compared with conventional low-rank tomography methods. Comments: Subjects: Quantum Physics (quant-ph); Machine Learning (cs.LG); Signal Processing (eess.SP); Numerical Analysis (math.NA); Optimization and Control (math.OC) MSC classes: 81P18, 15A69, 65F55 Cite as: arXiv:2609.09457 [quant-ph] (or arXiv:2609.09457v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.09457 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Shakir Showkat Sofi [view email] [v1] Tue, 8 Sep 2026 21:15:52 UTC (371 KB) Full-text links: Access Paper: View a PDF of the paper titled A Block Tensor Train Burer-Monteiro Framework for Low-Rank Quantum State Tomography, by Shakir Showkat Sofi and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 Change to browse by: cs cs.LG cs.NA eess eess.SP math math.NA math.OC 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?)