Dresden 2026 – scientific programme
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QI: Fachverband Quanteninformation
QI 5: Quantum Computing and Algorithms II
QI 5.8: Talk
Tuesday, March 10, 2026, 11:45–12:00, BEY/0137
From gradients to curvature: tensor-network Hessian-vector products for second-order Riemannian quantum circuit compression — •Isabel Nha Minh Le1,2, Roeland Wiersema3, and Christian B. Mendl1,2,4 — 1Technical University of Munich, School of Computation, Information and Technology, Boltzmannstraße 3, 85748 Garching, Germany — 2Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, 80799 Munich, Germany — 3Center for Computational Quantum Physics, Flatiron Institute, 162 Fifth Avenue, New York, NY 10010, USA — 4Technical University of Munich, Institute for Advanced Study, Lichtenbergstraße 2a, 85748 Garching, Germany
Riemannian optimization, combined with tensor network techniques, has shown strong potential for quantum circuit compression. However, existing approaches either rely solely on first-order gradient information [1] or are restricted to symmetry-invariant systems [2]. We introduce a tensor-network-based framework for efficiently computing second-order derivatives on Riemannian manifolds. By integrating these curvature estimates with in- and out-of-distribution generalization strategies from quantum machine learning [3], we develop a scalable second-order Riemannian optimization method for compressing quantum circuits.
[1] Quantum 9, 1833 (2025).
[2] J. Phys. A: Math. Theor. 57 135303 (2024).
[3] arXiv preprint arXiv:2409.16346 (2024).
Keywords: quantum simulation; trotterization; quantum circuit compression; quantum machine learning; tensor networks