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arXiv:2603.04339

Quantum error mitigation by hierarchy-informed sampling: chiral dynamics in the Schwinger model

Theo Saporiti, Oleg Kaikov, Vasily Sazonov, Mohamed Tamaazousti

quant-phhep-latSubmitted Mar 4, 2026• Announced Mar 5, 2026• 0 citations
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Abstract

Quantum simulations on current NISQ hardware are limited by its noisy nature, making efficient quantum error mitigation methods highly demanded. In this paper we introduce a novel mitigation scheme, applicable to arbitrary quantum simulations of time-dependent Hamiltonian dynamics on NISQ devices. The scheme uses a polynomial subset of extended qubit Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy equations as a sampling criterion of possible mitigated candidates for the quantum observables. We show that for favorable Hamiltonians the polynomial subset of BBGKY hierarchy equations leads to a polynomial overhead in both classical and quantum resources. We employ the method to mitigate simulations of the chiral magnetic effect (CME), a chiral feature of the Schwinger model. We empirically show the effectiveness of our scheme at recovering the real-time dynamics of the CME from noisy quantum simulations of the Schwinger model, for a range of different parameter values of the model. We numerically demonstrate a systematic reduction of quantum noise, together with an increasing noise reduction capability as the amount of BBGKY constraints grows.

Comments
17 pages, 8 figures, 1 table

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Quantum simulations on current NISQ hardware are limited by its noisy nature, making efficient quantum error mitigation methods highly demanded. In this paper we introduce a novel mitigation scheme, applicable to arbitrary quantum simulations of time-dependent Hamiltonian dynamics on NISQ devices. The scheme uses a polynomial subset of extended qubit Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy equations as a sampling criterion of possible mitigated candidates for the quantum observables. We show that for favorable Hamiltonians the polynomial subset of BBGKY hierarchy equations leads to a polynomial overhead in both classical and quantum resources. We employ the method to mitigate simulations of the chiral magnetic effect (CME), a chiral feature of the Schwinger model. We empirically show the effectiveness of our scheme at recovering the real-time dynamics of the CME from noisy quantum simulations of the Schwinger model, for a range of different parameter values of the model. We numerically demonstrate a systematic reduction of quantum noise, together with an increasing noise reduction capability as the amount of BBGKY constraints grows.
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Quantum error mitigation (QEM) is at the very heart of near-term quantum simulations and lattice gauge theories are no exceptions, rather their physical symmetries provide natural consistency checks on noise quantum states. In this work, we exploit the parity and fermion-number symmetries of a gauge theory, the (1+1)-dimensional Schwinger model, under depolarising noise and investigate symmetry verification under digital quantum simulation. We investigate two set-ups - symmetry- sector post-selection in adiabatic state preparation followed by real-time measurements of the chiral condensate and symmetry verification within a variational quantum eigensolver (VQE). In the first case, post-selection reduces the bias in the chiral condensate consistently removing up to 60% of the quantum noise induced error in our system. Motivated by the observed regularity of the residual bias (in the low-noise regime), we further introduce a global-noise calibration obtained from classically accessible smaller lattices and implemented on larger lattices recovering noiseless chiral condensate values within statistical uncertainty. However, in VQE, symmetry verification does not seem to generally improve the optimised parameters or the fidelity of the prepared states, although it reduces the bias in the estimated ground-state energy. This demonstates that improving a noisy cost-function estimator in variational algorithms does not necessarily improve the outcome of the algorithm. Our results show the strength of symmetry verification in different approaches while establishing that its usefulness critically depends on where it is applied in the computational workflow, and provide practical guidance for symmetry-assisted quantum error mitigation in quantum simulations of lattice gauge theories.
Quantum error mitigation (QEM) infers noiseless expectation values from noisy variants of a target quantum circuit. Unlike quantum error correction, QEM requires no additional hardware resources and is therefore routinely employed in experiments on contemporary quantum processors. QEM strategies based on agnostic noise amplification (ANA) are intrinsically resilient to temporal noise drift during the execution of the experiment, but their sampling cost (runtime overhead) remains a major practical bottleneck. In this work, we introduce the virtual noise scaling framework and combine it with layered mitigation to further enhance performance. While virtual noise scaling consistently reduces sampling overhead, we identify a specific noise threshold for the layered mitigation approach. When the noise level is above this threshold, layered mitigation decreases the sampling overhead; conversely, when below it, the overhead increases. Notably, this threshold is circuit-independent and depends solely on the number of layers. For strong noise, the combination of virtual noise scaling and layered mitigation yields several orders of magnitude reduction in sampling overhead compared with conventional zero-noise extrapolation post-processing. As a result, mitigation tasks that once seemed unrealistic are now challenging but achievable. The proposed approach is compatible with dynamic circuits and can be seamlessly integrated with error detection and quantum error correction schemes. In addition, it is also applicable to ANA-based mitigation of mid-circuit measurements and preparation errors. Our findings extend to any constant-step amplification factors and therefore also apply to probabilistic error amplification (PEA) QEM. We validate our post-processing approach by applying it to previously reported experimental data, where we observe a substantial improvement in mitigation efficiency and accuracy.
Analog quantum simulation has been proposed as an efficient approach for probing classically intractable many-body physics. In contrast to digital, gate-based quantum simulation, the analog approach involves configuring the quantum hardware to directly mimic the physics of the target system. This reduces the level of control required and can offer a degree of inherent robustness, but it comes at the cost that known error-handling techniques may be inapplicable. Accumulation of error is thus a major challenge facing medium-scale and large-scale analog quantum simulation with current and near-term noisy quantum (NISQ) devices. Here we propose a hybrid error mitigation scheme that can suppress general local Markovian noise in analog quantum simulators. We employ stochastic error mitigation for physical noise and use Richardson extrapolation to compensate for model estimation error. We numerically test the error mitigation scheme for an Ising-type Hamiltonian with energy relaxation and dephasing noise, and show an improvement of simulation accuracy by two orders. We assess the resource cost of our error mitigation scheme and conclude that analog quantum simulation at scale is feasible with NISQ hardware.