Bounded-Error Quantum Simulation via Hamiltonian and Lindbladian Learning

Year: 2026

Authors: Kraft T., Joshi MK., Lam WT., Olsacher T., Kranzl F., Franke J., Joshi LK., Blatt R., Smerzi A., Franza DS., Vermersch B., Kraus B., Roos CF., Zoller P.

Autors Affiliation: Tech Univ Munich, TUM Sch Nat Sci, Phys Dept, D-85748 Garching, Germany; Munich Ctr Quantum Sci & Technol MCQST, Schellingst 4, D-80799 Munich, Germany; Univ Innsbruck, Inst Theoret Phys, Innsbruck, Austria; Austrian Acad Sci, Inst Quantum Opt & Quantum Informat, Innsbruck, Austria; Univ Innsbruck, Inst Expt Phys, Innsbruck, Austria; Univ Grenoble Alpes, CNRS, LPMMC, Grenoble, France; Forschungszentrum Julich GmbH, Peter Grunberg Inst, Quantum Control PGI 8, D-52425 Julich, Germany; SISSA Int Sch Adv Studies, Trieste, Italy; CNR, INO, Largo Enrico Fermi 2, I-50125 Florence, Italy; LENS, Largo Enrico Fermi 2, I-50125 Florence, Italy; Univ Copenhagen, Dept Math Sci, Copenhagen, Denmark; Univ Copenhagen, Quantum Life Ctr, Copenhagen, Denmark; Quobly, Grenoble, France.

Abstract: Analog quantum simulators offer a route to exploring strongly correlated many-body dynamics beyond classical computation, but their predictive power remains limited by the absence of quantitative error estimation. Establishing rigorous uncertainty bounds is essential for elevating such devices from qualitative demonstrations to quantitative scientific tools. Here we introduce a general framework for bounded-error quantum simulation, which provides predictions for many-body observables with experimentally quantifiable uncertainties. The approach combines Hamiltonian and Lindbladian Learning-a statistically rigorous inference of the coherent and dissipative generators governing the dynamics-with the propagation of their uncertainties into the simulated observables, yielding confidence bounds directly derived from experimental data. We demonstrate this framework on trapped-ion quantum simulators implementing long-range Ising interactions with up to 51 ions. We analyze error bounds on two levels. First, we learn an open-system model from experimental data collected in an initial time window of quench dynamics, simulate the corresponding master equation, and quantitatively verify consistency between theoretical predictions and measured dynamics at long times. Second, we discuss short-time error bounds directly from experimental measurements alone, without relying on classical simulation-crucial for entering regimes of quantum advantage. In both cases, the learned models reproduce the experimental evolution within the predicted bounds, demonstrating quantitative reliability and internal consistency. By integrating statistical learning, open-system modeling, and precise experimental control, bounded-error quantum simulation provides a scalable foundation for trusted analog quantum computation, bridging the gap between experimental quantum platforms and predictive many-body physics. The techniques presented here directly extend to digital quantum simulation.

Journal/Review: PHYSICAL REVIEW X

Volume: 16 (3)      Pages from: 31037-1  to: 31037-26

More Information: W. T. L. and B. V. thank M. Filippone for useful discussions. T. K., T. O., B. K., and P. Z, acknowledge funding from the BMW Endowment Fund and from the European Union’s Horizon Europe research and innovation programme under the calls HORIZON-CL4-2022-QUANTUM-02-SGA via Grant Agreement No. 101113690 (PASQuanS2.1) and HORIZON-CL4-2021-DIGITAL-EMERGING-02-10 via Grant Agreement No. 101080085 (QCFD) . P. Z. thanks the support by Quantum Science Austria-quantA, an Austrian Excellence Programme funded by the Austrian Science Fund (FWF) [Grant DOI: 10.55776/COE1] . T. O. acknowledges support from the German Federal Ministry ofEducation and Research (BMBF) via the funding programme Quantum technologies-from basic research to market, project Grant No. 13N16073 (MUNIQC-Atoms) . W. T. L., B. V., and D. S. F. acknowledge funding from the French Plan France 2030 research programme HQI (Grant No. ANR-22-PNCQ-0002) . W. T. L. is additionally supported by the QuanTEdu-France programme (Grant No. ANR-22-CMAS-0001, France 2030) . D. S. F. acknowledges financial support from the Novo Nordisk Foundation (Grant No. NNF20OC0059939, Quantum for Life) and by the European Research Council (ERC) via Grant No. 101163938 (GIFNEQ) . L. K. J. acknowledges support from the European Union’s Horizon Europe program under the Marie Sklodowska Curie Action Project ETHOQS (Grant No. 101151139), and the support of the IQOQI, Innsbruck of the Austrian Academy of Sciences, during secondment of the ETHOQS project. M. K. J., F. K., J. F., R. B., and C. F. R. acknowledge funding from the European Union’s Horizon 2020 research and innovation programme under Grant Agreement No. 101113690 (PASQuanS2.1) , and via the Austrian Science Fund (FWF) through the SFB BeyondC (Grant-DOI 10.55776/F71) . P. Z. is a member of Q-SenSe at JILA, a National Science Foundation (NSF) Quantum Leap Challenge Institute focused on quantum sensing and engineering.
KeyWords: Lieb-robinson Bounds
DOI: 10.1103/s96t-n8tx