Inductive Graph Convolutional Quantum Process Tomography: A Scalable Geometric Deep Learning Approach

Inductive Graph Convolutional Quantum Process Tomography: A Scalable Geometric Deep Learning Approach | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Inductive Graph Convolutional Quantum Process Tomography: A Scalable Geometric Deep Learning Approach BOUAKER IMED This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9118683/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 6 You are reading this latest preprint version Abstract Quantum process tomography (QPT) is a fundamental task in quantum information science, yet it suffers from exponential scaling in the number of qubits. We introduce an inductive graph convolutional approach, IGC-QPT, that overcomes this limitation by exploiting the geometric structure of Choi matrices. The method constructs a graph based on a fast low-rank approximation of the Bures distance, then learns a GraphSAGE encoder to map measurement data to low-dimensional embeddings that preserve the local geometry of the process space. This enables efficient and accurate reconstruction of unknown quantum processes from limited measurements for systems up to seven qubits. Theoretical analysis provides sample complexity bounds with complete proofs, including a detailed analysis of the low-rank approximation error. Extensive numerical experiments on 2–7 qubit systems, with full statistical reporting, demonstrate that IGC-QPT significantly outperforms standard QPT (LS), compressed sensing (CS), and neural network methods (NN), achieving high fidelity with orders of magnitude speedup. A detailed discussion of assumptions, limitations, and practical considerations such as transfer learning for reducing training requirements is provided, along with robustness checks. Quantum process tomography Graph neural networks Geometric deep learning Choi matrix Bures distance Low-rank approximation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 16 Apr, 2026 Reviewers agreed at journal 16 Apr, 2026 Reviewers invited by journal 16 Apr, 2026 Editor assigned by journal 02 Apr, 2026 Submission checks completed at journal 16 Mar, 2026 First submitted to journal 13 Mar, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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