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arXiv:2007.01901 · PRX Quantum

Quantifying the Sensitivity to Errors in Analog Quantum Simulation

Pablo M. Poggi, Nathan Lysne, Kevin W. Kuper, Ivan Deutsch, Poul Jessen

Published Nov 2, 2020• 24 citations
arXivHTMLPDF

Abstract

Quantum simulators are widely seen as one of the most promising near-term applications of quantum technologies.However, it remains unclear to what extent a noisy device can output reliable results in the presence of unavoidable imperfections.Here we propose a framework to characterize the performance of quantum simulators by linking the robustness of measured quantum expectation values to the spectral properties of the output observable, which in turn can be associated with its macroscopic or microscopic character.We show that, under general assumptions and on average over all states, imperfect devices are able to reproduce the dynamics of macroscopic observables accurately, while the relative error in the expectation value of microscopic observables is much larger on average.We experimentally demonstrate the universality of these features in a state-of-the-art quantum simulator and show that the predicted behavior is generic for a highly accurate device, without assuming any detailed knowledge about the nature of the imperfections.

DOI
10.1103/prxquantum.1.020308

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Quantum simulators are widely seen as one of the most promising near-term applications of quantum technologies.However, it remains unclear to what extent a noisy device can output reliable results in the presence of unavoidable imperfections.Here we propose a framework to characterize the performance of quantum simulators by linking the robustness of measured quantum expectation values to the spectral properties of the output observable, which in turn can be associated with its macroscopic or microscopic character.We show that, under general assumptions and on average over all states, imperfect devices are able to reproduce the dynamics of macroscopic observables accurately, while the relative error in the expectation value of microscopic observables is much larger on average.We experimentally demonstrate the universality of these features in a state-of-the-art quantum simulator and show that the predicted behavior is generic for a highly accurate device, without assuming any detailed knowledge about the nature of the imperfections.
As uncorrected quantum processors grow in sophistication, many are being used for analog quantum simulation (AQS) of novel physics beyond the capabilities of classical devices. However, without the guarantee of bounded errors achieved by digitizing the computation, we do not know when and how much to trust an AQS result in the presence of inevitable imperfections. Here, we present the results of using our exper- iment as a testbed for studying the impact of errors on AQS. We have developed a small but highly-accurate processor over a 16-dimensional Hilbert space comprising the combined electron-nuclear spin of a single 133Cs atom in the electronic ground state. Advances in Eigenvalue-Only (EVO) optimal control enable us to repeatedly (>100) perform arbitrary unitary transformations in this space while maintaining accuracy on the device. We use this capability to simulate model systems known to exhibit features of interest, such as chaos and hypersensitivity (quantum kicked top) and quantum phase transitions (the transverse Ising and Lipkin-Meshkov-Glick mod- els). Experimental simulations show high fidelity of the quantum state and dynamical features in the presence of native imperfections. We discuss these results in the con- text of a new framework for quantifying the average sensitivity of simulator outcomes to errors. These theoretical and experimental results support the idea that AQS of ‘macroscopic’ observables (e.g., total magnetization) can be robust in the presence of errors, while observables tied to a specific quantum state (e.g., the fidelity) are not.
Analog quantum simulators (AQS) will likely be the first nontrivial application of quantum technology for predictive simulation. However, there remain questions regarding the degree of confidence that can be placed in the results of AQS since they do not naturally incorporate error correction. Specifically, how do we know whether an analog simulation of a quantum model will produce predictions that agree with the ideal model in the presence of inevitable imperfections? At the same time there is a widely held expectation that certain quantum simulation questions will be robust to errors and perturbations in the underlying hardware. Resolving these two points of view is a critical step in making the most of this promising technology. In this work we formalize the notion of AQS reliability by determining sensitivity of AQS outputs to underlying parameters, and formulate conditions for robust simulation. Our approach naturally reveals the importance of model symmetries in dictating the robust properties. To demonstrate the approach, we characterize the robust features of a variety of quantum many-body models.
Quantum simulation is a central application of near-term quantum devices, pursued in both analog and digital architectures. A key challenge for both paradigms is the effect of imperfections and noise on predictive power. In this work, we present a rigorous and physically transparent comparison of the stability of digital and analog quantum simulators under a variety of perturbative noise models. We provide rigorous worst- and average-case error bounds for noisy quantum simulation of local observables. We find that the two paradigms show comparable scaling in the worst case, while exhibiting different forms of enhanced error cancellation on average. We further analyze Gaussian and Brownian noise processes, deriving concentration bounds that capture typical deviations beyond worst-case guarantees. These results provide a unified framework for quantifying the robustness of noisy quantum simulations and identify regimes where digital methods have intrinsic advantages and when we can see similar behavior.
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.
Abstract Quantum simulation is a central application of near-term quantum devices, pursued in both analog and digital architectures. A key challenge for both paradigms is the effect of imperfections and noise on predictive power. In this work, we present a rigorous and physically transparent comparison of the stability of digital and analog quantum simulators under a variety of perturbative noise models. We provide rigorous worst- and average-case error bounds for noisy quantum simulation of local observables. We find that the two paradigms show comparable scaling in the worst case, while exhibiting different forms of enhanced error cancellation on average. We further analyze Gaussian and Brownian noise processes, deriving concentration bounds that capture typical deviations beyond worst-case guarantees. These results provide a unified framework for quantifying the robustness of noisy quantum simulations and identify regimes where digital methods have intrinsic advantages and when we can see similar behavior.
Analog quantum processors based on Rydberg atom arrays are a powerful platform for many-body quantum simulation, combinatorial optimization, and graph machine learning. As these devices become increasingly accessible, establishing confidence in their outputs requires predictive models that quantitatively connect microscopic hardware imperfections to empirical results. Here, we present a noise-aware emulation framework that propagates the dominant noise mechanisms throughout the full computation cycle to predict device behavior. We validate the framework by benchmarking two representative protocols, quantum annealing and post-quench dynamics, on three Pasqal quantum processors where classical simulations still provide ground truth. Across all three devices, the measured observables fall within the uncertainty envelopes predicted by the emulator. Beyond reproducing the data, the framework isolates which physical mechanism dominates in each operating regime, provides quantitative guidance for algorithm design and hardware improvements, and establishes a foundation for verifying analog processors in regimes beyond classical reach.