I will discuss Hamiltonian and Liouvillian learning techniques for analog quantum simulation from non-equilibrium quench dynamics in the limit of weakly dissipative many-body systems [1]. 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. I will explain a general framework for bounded-error quantum simulation, which provides predictions for many-body observables with experimentally quantifiable uncertainties [2]. 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. I will present the results of a demonstration of this framework on trapped-ion quantum simulators implementing long-range Ising interactions with up to 51 ions.
Ref:
[1] Bounded-Error Quantum Simulation via Hamiltonian and Lindbladian Learning,
Tristan Kraft, Manoj K. Joshi, William Lam, Tobias Olsacher, Florian Kranzl, Johannes Franke, Lata Kh Joshi, Rainer Blatt, Augusto Smerzi, Daniel Stilck França, Benoît Vermersch, Barbara Kraus, Christian F. Roos, Peter Zoller, https://arxiv.org/abs/2511.23392
[2] Hamiltonian and Liouvillian learning in weakly-dissipative quantum many-body systems, Tobias Olsacher, Tristan Kraft, Christian Kokail, Barbara Kraus, Peter Zoller, https://arxiv.org/abs/2405.06768