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arXiv:2601.05952 · Nature Communications

Continuous-time noise mitigation in analogue quantum simulation

Gabriele Bressanini, Yue Ma, Hyukjoon Kwon, M. S. Kim

quant-phSubmitted Jan 9, 2026• Announced Jan 12, 2026• 0 citations
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Abstract

Analogue quantum simulators offer a promising route to explore quantum many-body dynamics beyond classical reach in the near term. However, their vulnerability to noise limits the accuracy of simulations. Here, we establish a new framework for mitigating noise in analogue quantum simulation, operating in a time-continuous manner. To our knowledge, this is the first protocol that is fully analogue and that achieves exact noise cancellation. Our method requires a small number of ancillary qubits, whose interaction with the system$-$combined with classical post-processing of joint measurement data$-$is tailored to cancel the effect of noise. Furthermore, the protocol is Hamiltonian-independent, robust to realistic ancilla noise, and avoids any discretization, preserving the continuous-time nature of the system's dynamics. This work opens a new direction for achieving high-fidelity analogue quantum simulation in the presence of noise.

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Analogue quantum simulators offer a promising route to explore quantum many-body dynamics beyond classical reach in the near term. However, their vulnerability to noise limits the accuracy of simulations. Here, we establish a new framework for mitigating noise in analogue quantum simulation, operating in a time-continuous manner. To our knowledge, this is the first protocol that is fully analogue and that achieves exact noise cancellation. Our method requires a small number of ancillary qubits, whose interaction with the system−-−combined with classical post-processing of joint measurement data−-−is tailored to cancel the effect of noise. Furthermore, the protocol is Hamiltonian-independent, robust to realistic ancilla noise, and avoids any discretization, preserving the continuous-time nature of the system's dynamics. This work opens a new direction for achieving high-fidelity analogue quantum simulation in the presence of noise.
Analog quantum simulation is a promising path towards solving classically intractable problems in many-body physics on near-term quantum devices. However, the presence of noise limits the size of the system and the length of time that can be simulated. In our work, we consider an error model in which the actual Hamiltonian of the simulator differs from the target Hamiltonian we want to simulate by small local perturbations, which are assumed to be random and unbiased. We analyze the error accumulated in observables in this setting and show that, due to stochastic error cancellation, with high probability the error scales as the square root of the number of qubits instead of linearly. We explore the concentration phenomenon of this error as well as its implications for local observables in the thermodynamic limit. Moreover, we show that stochastic error cancellation also manifests in the fidelity between the target state at the end of time-evolution and the actual state we obtain in the presence of noise. This indicates that, to reach a certain fidelity, more noise can be tolerated than implied by the worst-case bound if the noise comes from many statistically independent sources.
Quantum simulation of dynamics is an important goal in the noisy intermediate-scale quantum era, within which quantum error mitigation may be a viable path towards modifying or eliminating the effects of noise. Most studies on quantum error mitigation have focused on the resource cost due to its exponential scaling in the circuit depth. Methods such as probabilistic error cancellation rely on discretizing the evolution into finite time steps and applying the mitigation layer after each time step, modifying only the noise part without any Hamiltonian dependence. This may lead to Trotter-like errors in the simulation results even if the error mitigation is implemented ideally, which means that the number of samples is taken as infinite. Here we analyze the aforementioned errors which have been largely neglected before. We show that they are determined by the commutating relations between the superoperators of the unitary part, the device noise part, and the noise part of the open dynamics to be simulated. We include both digital quantum simulation and analog quantum simulation setups and consider defining the ideal error mitigation map both by exactly inverting the noise channel and by approximating it to first order in the time step. We use single-qubit toy models to numerically demonstrate our findings. Our results illustrate fundamental limitations of applying probabilistic error cancellation in a stepwise manner to continuous dynamics, thus motivating the investigations of truly time-continuous error cancellation methods. Published by the American Physical Society 2024
The pursuit of high-fidelity digital quantum simulation is fundamentally constrained by the inevitable presence of noise in current and near-term quantum processors. While quantum error correction ultimately promises fault-tolerance, its substantial qubit overhead renders it impractical for the noisy intermediate-scale quantum (NISQ) era. This research addresses the critical gap between hardware imperfections and simulation accuracy by designing systematic, resource-efficient machine learning (ML) error-mitigation protocols tailored specifically for digital quantum simulation. Unlike generic error-suppression methods, our approach exploits the unique structural properties of simulated quantum dynamics—including time-translation invariance, locality of interactions, and conserved quantities—to inform the training of lightweight neural networks and Gaussian process regressors. We develop a hybrid framework that combines randomized compiling with data-driven noise-inversion models, enabling real-time estimation and subtraction of both coherent and incoherent errors without exponential sampling overhead. Through extensive numerical benchmarks on spin-chain and Fermi-Hubbard models, we demonstrate that our ML protocols achieve up to an order-of-magnitude reduction in infidelity compared to standard probabilistic error cancellation and zero-noise extrapolation, while requiring fewer calibration circuits. Furthermore, we introduce an adaptive online learning scheme that continuously refines the mitigation model during the simulation runtime, automatically adjusting to time-dependent drift in hardware noise. Our results establish a practical pathway toward scalable, high-accuracy quantum simulations on existing devices, with implications for condensed matter physics, quantum chemistry, and the development of quantum advantage benchmarks.
The pursuit of quantum advantage is driving the co-evolution of quantum processors and classical simulation methods. Despite advances in scale and quality, the accuracy of quantum simulation is ultimately limited by error rates and sampling overheads. Similarly, while classical simulation methods such as Pauli propagation have made remarkable progress, their accuracy is ultimately limited by the exponential growth of operator paths and the truncations needed to control memory and runtime. Here we show that these complementary limitations can be mitigated by embedding Pauli propagation within a hybrid error-mitigation framework that reduces quantum sampling overhead while achieving lower truncation errors with fewer classical resources than traditional Pauli propagation alone. In this framework, a target observable is classically propagated through noise-canceling inverse channels, producing a modified observable that is measured directly on a quantum processor. We prototype two implementations and benchmark their performance numerically on canonical models that challenge traditional Pauli propagation. We also perform experiments on a quantum processor using 56 superconducting qubits, revealing the tradeoffs of their respective truncation strategies. These results illustrate how classical and quantum resources can be orchestrated to extend observable estimation beyond the limits of either approach alone, providing a foundation for quantum-centric supercomputing and future demonstrations of quantum advantage.
Analog quantum simulators have provided key insights into quantum many-body dynamics. However, in such systems, both coherent and incoherent errors limit their scalability, hindering simulations in regimes that challenge classical simulations. In this work, we introduce an error mitigation technique that addresses and effectively suppresses a key source of error in leading simulator platforms: shot-to-shot fluctuations in the parameters for the Hamiltonian governing the system dynamics. We rigorously prove that amplifying this shot-to-shot noise and extrapolating to the zero-noise limit recovers noiseless results for realistic noise distributions. Experimentally, we demonstrate this technique on a 27-ion trapped-ion quantum simulator, extending the two-qubit exchange oscillation lifetime threefold. Numerically, we predict a significant enhancement in the effective many-body coherence time for Rydberg atom arrays under realistic conditions. Our scheme provides a possible route towards extending the effective coherence time in analog quantum experiments, enabling deeper explorations of quantum many-body dynamics.
While non-Hermitian Hamiltonians enable exotic dynamical phenomena, implementing their nonunitary time evolution on near-term quantum devices remains challenging. We propose a hardware-friendly protocol that simulates non-Hermitian dynamics without ancillas, controlled time evolution, or continuous monitoring. The protocol combines a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) evolution via classical Gaussian white-noise averaging with stochastic quantum error mitigation (QEM) to cancel the jump contribution at the level of expectation values. The mitigation layer uses only single-qubit operations. We validate the method through numerical simulations of an asymmetric-hopping model and an open {\it XXZ} spin chain with non-Hermitian boundary fields. Our work provides a programmable and ancilla-free framework for investigating exotic dynamics beyond the class of completely positive and trace-preserving dynamics using QEM.