Absence of poor local minima in matrix product states
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Quantum Physics arXiv:2606.09988 (quant-ph) [Submitted on 8 Jun 2026] Title:Absence of poor local minima in matrix product states Authors:Hao-Kai Zhang, Chenghong Zhu, Shuo Liu, Shi-Xin Zhang, Tao Xiang View a PDF of the paper titled Absence of poor local minima in matrix product states, by Hao-Kai Zhang and 4 other authors View PDF HTML (experimental) Abstract:Quantum circuits suffer from severe trainability issues: even shallow circuits are swamped with poor local minima. Yet matrix product states (MPS), which can be prepared by sequential circuits, are remarkably trainable in practice -- as demonstrated by decades of successful density matrix renormalization group calculations. In this work, we resolve this apparent paradox by proving that the energy landscapes of MPS are free from poor local minima, under the same setting where brickwork circuits are not. The key insight is that the gauge freedom of MPS creates an effective local overparametrization that causes local minima to concentrate near the global minimum, analogous to overparametrized classical neural networks. We rigorously prove that the local minimum distribution of the MPS energy landscape is invariant under moves of the orthogonality center. Numerical experiments further confirm that the optimization of sequential circuits converges to near-optimal solutions even for random Hamiltonians, in stark contrast to brickwork circuits. Our findings highlight the pivotal role of effective local overparametrization in determining trainability, providing a valuable guide for overcoming the trainability bottleneck of variational quantum algorithms. Comments: Subjects: Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Strongly Correlated Electrons (cond-mat.str-el); Computational Physics (physics.comp-ph) Cite as: arXiv:2606.09988 [quant-ph] (or arXiv:2606.09988v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.09988 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Hao-Kai Zhang [view email] [v1] Mon, 8 Jun 2026 18:00:02 UTC (4,163 KB) Full-text links: Access Paper: View a PDF of the paper titled Absence of poor local minima in matrix product states, by Hao-Kai Zhang and 4 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 Change to browse by: cond-mat cond-mat.dis-nn cond-mat.str-el physics physics.comp-ph 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?)