Bounded-Error Quantum Simulation via Hamiltonian and Lindbladian Learning

• URL: http://arxiv.org/abs/2511.23392v1
• Date: Fri, 28 Nov 2025 17:33:59 GMT
• Title: Bounded-Error Quantum Simulation via Hamiltonian and Lindbladian Learning
• Authors: 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,
• Abstract summary: We introduce a general framework for bounded-error quantum simulation.<n>It provides predictions for many-body observables with experimentally quantifiable uncertainties.<n>We demonstrate this framework on trapped-ion quantum simulators implementing long-range Ising interactions with up to 51 ions.
• Score: 1.7515811671331791
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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, and validate it where classical comparison is possible. 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 establish error bounds directly from experimental measurements alone, without relying on classical simulation--crucial for entering regimes of quantum advantage. The learned models reproduce the experimental evolution within the predicted bounds, demonstrating quantitative reliability and internal consistency. Bounded-error quantum simulation provides a scalable foundation for trusted analog quantum computation, bridging the gap between experimental platforms and predictive many-body physics. The techniques presented here directly extend to digital quantum simulation.

Related papers

• Majorana string simulation of nonequilibrium dynamics in two-dimensional lattice fermion systems [0.8739101659113157]
  We introduce a Heisenberg-picture algorithm that propagates observables expressed in a Majorana-string basis using a truncation scheme.<n>We benchmark our approach on one- and two-dimensional Fermi-Hubbard quenches.
  arXiv  Detail & Related papers  (2025-11-04T18:30:35Z)
• Learning Minimal Representations of Many-Body Physics from Snapshots of a Quantum Simulator [0.08796261172196741]
  We develop a machine learning approach based on a variational autoencoder (VAE) to analyze interference measurements of Bose gases.<n>Applying to non-equilibrium protocols, the latent space uncovers signatures of frozen-in solitons following rapid cooling.<n>Results demonstrate that generative models can extract physically interpretable variables directly from noisy and sparse experimental data.
  arXiv  Detail & Related papers  (2025-09-17T08:38:46Z)
• Error mitigation of shot-to-shot fluctuations in analog quantum simulators [46.54051337735883]
  We introduce an error mitigation technique that addresses shot-to-shot fluctuations in the parameters for the Hamiltonian governing the system dynamics.<n>We rigorously prove that amplifying this shot-to-shot noise and extrapolating to the zero-noise limit recovers noiseless results for realistic noise distributions.<n> Numerically, we predict a significant enhancement in the effective many-body coherence time for Rydberg atom arrays under realistic conditions.
  arXiv  Detail & Related papers  (2025-06-19T18:00:00Z)
• Ensemble models outperform single model uncertainties and predictions for operator-learning of hypersonic flows [43.148818844265236]
  Training scientific machine learning (SciML) models on limited high-fidelity data offers one approach to rapidly predict behaviors for situations that have not been seen before. High-fidelity data is itself in limited quantity to validate all outputs of the SciML model in unexplored input space. We extend a DeepONet using three different uncertainty mechanisms: mean-variance estimation, evidential uncertainty, and ensembling.
  arXiv  Detail & Related papers  (2023-10-31T18:07:29Z)
• Fast and converged classical simulations of evidence for the utility of quantum computing before fault tolerance [0.0]
  A recent quantum simulation of observables of the kicked Ising model on 127 qubits implemented circuits exceeds the capabilities of exact classical simulation. We show that several approximate classical methods, based on sparse Pauli dynamics and tensor network algorithms, can simulate these observables orders of magnitude faster than the quantum experiment.
  arXiv  Detail & Related papers  (2023-08-09T17:15:17Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• Importance sampling for stochastic quantum simulations [68.8204255655161]
  We introduce the qDrift protocol, which builds random product formulas by sampling from the Hamiltonian according to the coefficients. We show that the simulation cost can be reduced while achieving the same accuracy, by considering the individual simulation cost during the sampling stage. Results are confirmed by numerical simulations performed on a lattice nuclear effective field theory.
  arXiv  Detail & Related papers  (2022-12-12T15:06:32Z)
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics [62.997667081978825]
  We show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality. We show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators.
  arXiv  Detail & Related papers  (2022-06-03T18:00:02Z)
• Propagation of errors and quantitative quantum simulation with quantum advantage [0.0]
  Many-body quench dynamics is one of the most promising candidates for early practical quantum advantage. We analyse the requirements for quantitatively reliable quantum simulation beyond the capabilities of existing classical methods. We conclude for models that are directly implementable that regimes of practical quantum advantage are attained in current experiments with analogue simulators.
  arXiv  Detail & Related papers  (2022-04-28T17:05:51Z)
• Benchmarking a novel efficient numerical method for localized 1D Fermi-Hubbard systems on a quantum simulator [0.0]
  We show that a quantum simulator can be used to in-effect solve for the dynamics of a many-body system. We use a neutral-atom Fermi-Hubbard quantum simulator with $L_textexpsimeq290$ lattice sites to benchmark its performance. We derive a simple prediction of the behaviour of interacting Bloch oscillations for spin-imbalanced Fermi-Hubbard systems.
  arXiv  Detail & Related papers  (2021-05-13T16:03:11Z)
• Preparing random states and benchmarking with many-body quantum chaos [48.044162981804526]
  We show how to predict and experimentally observe the emergence of random state ensembles naturally under time-independent Hamiltonian dynamics. The observed random ensembles emerge from projective measurements and are intimately linked to universal correlations built up between subsystems of a larger quantum system. Our work has implications for understanding randomness in quantum dynamics, and enables applications of this concept in a wider context.
  arXiv  Detail & Related papers  (2021-03-05T08:32:43Z)
• Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond [46.39654665163597]
  We report on experimental tests of topological defect formation via the one-dimensional transverse-field Ising model. We find that the quantum simulator results can indeed be explained by the KZM for open-system quantum dynamics with phase-flip errors. This implies that the theoretical predictions of the generalized KZM theory, which assumes isolation from the environment, applies beyond its original scope to an open system.
  arXiv  Detail & Related papers  (2020-01-31T02:55:35Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.