SWAP-Network Routing and Spectral Qubit Ordering for MPS Imaginary-Time Optimization

Quantum Physics arXiv:2511.02980 (quant-ph) [Submitted on 4 Nov 2025] Title:SWAP-Network Routing and Spectral Qubit Ordering for MPS Imaginary-Time Optimization Authors:Erik M. Åsgrim, Stefano Markidis View a PDF of the paper titled SWAP-Network Routing and Spectral Qubit Ordering for MPS Imaginary-Time Optimization, by Erik M. {\AA}sgrim and Stefano Markidis View PDF HTML (experimental) Abstract:We propose a quantum-inspired combinatorial solver that performs imaginary-time evolution (ITE) on a matrix product state (MPS), incorporating non-local couplings through structured SWAP networks and spectral qubit mapping of logical qubits. The SWAP networks, composed exclusively of local two-qubit gates, effectively mediate non-local qubit interactions. We investigate two distinct network architectures based on rectangular and triangular meshes of SWAP gates and analyze their performance in combination with spectral qubit ordering, which maps logical qubits to MPS sites based on the Laplacian of the logical qubit connectivity graph. The proposed framework is evaluated on synthetic MaxCut instances with varying graph connectivity, as well as on a dynamic portfolio optimization problem based on real historical asset data involving 180 qubits. On certain problem configurations, we observe an over 20$\times$ reduction in error when combining spectral ordering and triangular SWAP networks compared to optimization with shuffled qubit ordering. Furthermore, an analysis of the entanglement entropy during portfolio optimization reveals that spectral qubit ordering not only improves solution quality but also enhances the total and spatially distributed entanglement within the MPS. These findings demonstrate that exploiting problem structure through spectral mapping and efficient routing networks can substantially enhance the performance of tensor-network-based optimization algorithms. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2511.02980 [quant-ph] (or arXiv:2511.02980v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2511.02980 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Erik M. Åsgrim [view email] [v1] Tue, 4 Nov 2025 20:37:26 UTC (1,035 KB) Full-text links: Access Paper: View a PDF of the paper titled SWAP-Network Routing and Spectral Qubit Ordering for MPS Imaginary-Time Optimization, by Erik M. {\AA}sgrim and Stefano MarkidisView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-11 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)