A Validation Framework for Quantum Simulation of Spin Dynamics against Inelastic Neutron Scattering and Classical Simulation
Gilles Buchs, Elaine Wong, Anshumitra Baul, Kathleen E. Hamilton, Arnab Banerjee, Stephan Eidenbenz, Gábor B. Halász, Paul Kairys, Keerthi Kumaran, Thomas Maier, Thomas Naughton, Elijah Pelofske, Vincent Russo, Allen Scheie, Yigit Subasi, D. Alan Tennant, Akram Touil, Travis S. Humble, Andrew T. Sornborger
quant-phSubmitted Jul 2, 2026• Announced Jul 3, 2026• 0 citations• Revised Oct 12, 2026 (v2)
Establishing quantum simulations as reliable tools for materials research requires quantitative validation against experiments and, where available, classical many-body calculations. For dynamical spin response, such validation remains challenging because experiment, classical simulation, and quantum simulation do not produce the same native observables. This challenge is increasingly relevant as quantum simulation protocols for dynamical response progress from theory to hardware-level benchmarking against neutron scattering data. The longer-term goal is to extend validation to classically intractable regimes accessible through future fault-tolerant implementations. Here, we develop a cross-pipeline validation framework for quantum simulation of dynamical spin response, using inelastic neutron scattering and classical many-body simulation as complementary experimental and computational anchors. The framework brings these pipelines to common momentum- and energy-resolved comparison levels through explicit forward and inverse observable maps, propagates uncertainty via covariance matrices or resampling, tests robustness to structured distortion, and evaluates agreement using a hierarchy of complementary metric families. It distinguishes stochastic uncertainty from robustness-induced distortion, carries both through the comparison chain, and uses the resulting metric-level uncertainty and distortion information to support layered validation at the pipeline, solver, and model levels. We also introduce actuator-aware feedback logic to improve agreement without obscuring the physical origin of any remaining mismatch. We close by outlining future extensions of this methodology, including upstream uncertainty and distortion modeling, adaptive feedback, asymmetric validation beyond full classical benchmarking, fault-tolerant workflows, and community infrastructure for reproducible validation.
Establishing quantum simulations as reliable tools for materials research requires quantitative validation against experiments and, where available, classical many-body calculations. For dynamical spin response, such validation remains challenging because experiment, classical simulation, and quantum simulation do not produce the same native observables. This challenge is increasingly relevant as quantum simulation protocols for dynamical response progress from theory to hardware-level benchmarking against neutron scattering data. The longer-term goal is to extend validation to classically intractable regimes accessible through future fault-tolerant implementations. Here, we develop a cross-pipeline validation framework for quantum simulation of dynamical spin response, using inelastic neutron scattering and classical many-body simulation as complementary experimental and computational anchors. The framework brings these pipelines to common momentum- and energy-resolved comparison levels through explicit forward and inverse observable maps, propagates uncertainty via covariance matrices or resampling, tests robustness to structured distortion, and evaluates agreement using a hierarchy of complementary metric families. It distinguishes stochastic uncertainty from robustness-induced distortion, carries both through the comparison chain, and uses the resulting metric-level uncertainty and distortion information to support layered validation at the pipeline, solver, and model levels. We also introduce actuator-aware feedback logic to improve agreement without obscuring the physical origin of any remaining mismatch. We close by outlining future extensions of this methodology, including upstream uncertainty and distortion modeling, adaptive feedback, asymmetric validation beyond full classical benchmarking, fault-tolerant workflows, and community infrastructure for reproducible validation.
Realistic simulation of quantum materials is a central goal of quantum computation. Although quantum processors have advanced rapidly in scale and fidelity, it has remained unclear whether pre-fault-tolerant devices can perform quantitatively reliable material simulations. We demonstrate that a superconducting quantum processor operating on up to 50 qubits can already produce meaningful, quantitative comparisons with inelastic neutron-scattering measurements of KCuF3, a canonical realization of a gapless Luttinger liquid system with a strongly correlated ground state and a spectrum of emergent spinons. The quantum simulation is enabled by a quantum-classical workflow for computing dynamical structure factors (DSFs). The resulting spectra are benchmarked against experimental measurements using multiple metrics, highlighting the impact of circuit depth and circuit fidelity on simulation accuracy. Finally, we extend our simulations to a 1D XXZ Heisenberg model with next-nearest-neighbor (NNN) interactions and a strong anisotropy, producing a gapped excitation spectrum, which could be used to describe the CsCoX3 compounds above the Néel temperature. Our results establish a framework for computing DSFs for quantum materials in classically challenging regimes of strong entanglement and long-range interactions, enabling quantum simulations that are directly testable against laboratory measurements.
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.
The dynamical structure factor is a central observable in condensed-matter physics, providing direct insight into the excitation spectrum and dynamical response of quantum materials. While it is traditionally accessed in real materials through inelastic neutron scattering, recent works have shown that analogous information can be extracted in quantum simulators using suitable dynamical protocols. So far, these approaches have been demonstrated mainly in paradigmatic integrable one-dimensional models. In this work, we use numerical emulations of a neutral-atom quantum processing unit to assess the feasibility of measuring the dynamical structure factor in a broader class of Ising-like spin systems. Beyond the standard one-dimensional transverse-field Ising chain, we benchmark the protocol in chains with dimerized interactions and in the two-dimensional transverse-field Ising model, where spectral properties are difficult to access with classical numerical methods at large scales. We further analyze the robustness of the protocol under realistic experimental conditions, including finite simulation times, pulse modulation, positional disorder, and laser noise. Our results show that neutral-atom quantum simulators can provide a practical route to probing dynamical response functions in regimes where classical simulations become increasingly demanding, paving the way toward experimental implementation.
While quantum computers promise to solve classically intractable problems, identifying the point at which fault-tolerant quantum computation outperforms the best classical algorithms for practical applications remains an outstanding challenge. Here we establish a concrete quantum-classical crossover for quantum many-body dynamics under realistic hardware conditions. We introduce a scalable fault-tolerant framework that combines coherent observable estimation with a space-time-efficient implementation of non-Clifford rotations, suppressing the residual logical errors that limit existing partially fault-tolerant approaches. A benchmark against state-of-the-art tensor-network and variational Monte Carlo algorithms reveals a concrete crossover for mixed-field Ising dynamics at modest system sizes. For a physical error rate of p=10−3, fault-tolerant simulation requires approximately 2 hours and 3.7×105 physical qubits for a 100-site 1D system, whereas tensor network approaches would require about 100 years. For 2D models, where rapid entanglement growth limits the classical evolution time, we project quantum runtimes within minutes. A physical error rate of p=10−4 leads to at least an order of magnitude reduction in qubit count (3.1×104 physical qubits) and runtime (minutes for 1D and seconds for 2D). The reduction in quantum runtime arises from our improved rotation-state injection and co-design of quantum error correction and observable-estimation protocols, which jointly suppress logical-error accumulation and reduce sampling overhead. Our results establish a scalable route towards practical quantum advantage and identify quantitative engineering targets for future fault-tolerant architectures.
Version 6.1 develops an integral framework for an analog quantum simulator of spin modelsbased on programmable superconducting-qubit arrays.The principal objective is not merely to construct a quantum device, but to establish atraceable mappingcontrol parameters −→ Hreal −→ quantum evolution −→ observables −→ classical reference.The framework supports transverse-field Ising, XY, XXZ, Heisenberg, long-range, anddisordered spin Hamiltonians.Version 6.1 introduces an explicit Hamiltonian- identification layer between hardwarecalibration and scientific validation.The realized Hamiltonian is decomposed into target terms, static calibration errors, dynamiccontrol errors, crosstalk, leakage, decoherence, and residual unwanted interactions.Validation is organized hierarchically:1. hardware calibration;2. Hamiltonian identification;3. state-preparation validation;4. readout calibration;5. static observable validation;6. dynamical observable validation;7. finite-size benchmarking;8. statistical equivalence testing;9. cross-device reproducibility;10. independent analytical reproduction. The statistical framework replaces the inadequate criterion of “statistical significance ofagreement” with an equivalence framework based on preregistered tolerances.The primary hypothesis is therefore formulated using two one-sided tests (TOST) or anequivalent confidence interval criterion:|∆O| < ϵO.Version 6.1 additionally specifies:• a supplementary Bayesian posterior probability of equivalence as a robustness check;• an explicit distinction between engineering no-go and physical falsification.The framework also specifies negative controls, positive controls, blind analysis, lockedanalysis code, exclusion rules, uncertainty propagation, data provenance, and reproducibilityrequirements.No experimental result or quantum advantage is claimed.
Quantum computing offers a new, orthogonal direction for investigating fundamental physics, extending beyond classical numerical methods and conventional observables. Realizing this potential requires directly confronting the noise limiting currently available quantum computers. Progress rests on advancing algorithms, interpreting their results, and managing their errors together. This thesis presents several advancements in the use of quantum simulation and quantum information to probe fundamental physics.
The first is in the use of quantum computers to simulate collisions in quantum field theories. Central to these simulations are new wavepacket preparation, time evolution, and error mitigation techniques, which allow for simulations with some of the largest effective circuit volumes to date. These methods enable the first quantum simulation providing numerical evidence for inelastic particle production, a key process in fundamental physics.
The second advancement centers on the role quantum-information-theoretic quantities play in physical processes. Beyond mere correlations with the physics of the process, entanglement and magic are shown to probe the interactions present in scattering and hadronization dynamics.
A precision study requires a complete quantification of algorithmic and hardware uncertainties, an outstanding goal as quantum simulations mature. The third advancement in this thesis addresses error management. A framework minimizing the effect of algorithmic errors in analog quantum simulations is presented. In a step toward fault tolerance, error detection in encoded quantum simulations is shown to improve estimation of local observables relative to unencoded runs.
Together, the developments in this thesis mark practical progress toward fault-tolerant quantum simulations of fundamental physics capable of scientific discovery.