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arXiv:2605.28342

Low-cost quantum error mitigation via auxiliary qubit return validation

Gilad Kishony, Avi Elazari, Ron Cohen, Lior Gazit

quant-phSubmitted May 27, 2026• Announced May 28, 2026• 0 citations
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Abstract

We introduce a low-overhead technique for quantum error mitigation based on post-selection using auxiliary qubit measurements. The method exploits the structural property that, in an error-free computation, auxiliary qubits are often expected to return to the zero state after use. By selectively measuring these qubits at carefully chosen points in the circuit, erroneous shots can be identified and discarded, improving result fidelity with minimal hardware overhead. To account for circuit noise, including measurement errors, we analyze the likelihood that a measurement outcome indicates a corrupted shot. This analysis is informed by the measurement's backward light cone, namely the set of circuit operations that could affect the outcome. Shots whose auxiliary measurement outcomes imply a corruption likelihood above a tunable threshold are rejected. Simulations show that the method reduces the false-negative rate by approximately 10% while discarding only approximately 1% of valid shots. The threshold controls the bias-variance tradeoff inherent to post-selection, allowing the method to be adapted to the fidelity and sampling requirements of different applications.

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Mitigating measurement errors in multiqubit experiments

Sergey B. Bravyi, Sarah Sheldon, Abhinav Kandala +2 more

Reducing measurement errors in multiqubit quantum devices is critical for performing any quantum algorithm. Here we show how to mitigate measurement errors by a classical postprocessing of the measured outcomes. Our techniques apply to any experiment where measurement outcomes are used for computing expected values of observables. Two error-mitigation schemes are presented based on tensor product and correlated Markovian noise models. Error rates parametrizing these noise models can be extracted from the measurement calibration data using a simple formula. Error mitigation is achieved by applying the inverse noise matrix to a probability vector that represents the outcomes of a noisy measurement. The error-mitigation overhead, including the number of measurements and the cost of the classical postprocessing, is exponential in $\ensuremath{\epsilon}n$, where $\ensuremath{\epsilon}$ is the maximum error rate and $n$ is the number of qubits. We report experimental demonstration of our error-mitigation methods on IBM Quantum devices using stabilizer measurements for graph states with $n\ensuremath{\le}12$ qubits and entangled 20-qubit states generated by low-depth random Clifford circuits.

arXiv:2006.14044•Physical Review A•Apr 9, 2021•335 citations
We introduce a low-overhead technique for quantum error mitigation based on post-selection using auxiliary qubit measurements. The method exploits the structural property that, in an error-free computation, auxiliary qubits are often expected to return to the zero state after use. By selectively measuring these qubits at carefully chosen points in the circuit, erroneous shots can be identified and discarded, improving result fidelity with minimal hardware overhead.
To account for circuit noise, including measurement errors, we analyze the likelihood that a measurement outcome indicates a corrupted shot. This analysis is informed by the measurement's backward light cone, namely the set of circuit operations that could affect the outcome. Shots whose auxiliary measurement outcomes imply a corruption likelihood above a tunable threshold are rejected.
Simulations show that the method reduces the false-negative rate by approximately 10% while discarding only approximately 1% of valid shots. The threshold controls the bias-variance tradeoff inherent to post-selection, allowing the method to be adapted to the fidelity and sampling requirements of different applications.
We present a simple, malleable and low-overhead approach for improving generic biased quantum error mitigation (QEM) methods, achieving up to 15% fidelity improvements over standard QEM on 100-qubit circuits with up to 2000 entangling gates. We do so by constructing verifiable benchmark circuits which mirror the application circuit's native-gate structure and thus noise profile. These circuits can be used to benchmark and mitigate the bias of the underlying error mitigation method, requiring only the application circuit and hardware native gate set. We present two methods for generating benchmark circuits; one is agnostic to the target hardware at the expense of a small overhead of single-qubit gates, while the other is specific to the IBM superconducting hardware and has no gate overhead. As a corollary, we introduce benchmarked-noise zero-noise extrapolation (bnZNE) as a simple adaptation of zero-noise extrapolation (ZNE), one of the most popular error mitigation methods. We consider as an example the bias-mitigated ZNE and bnZNE of Trotterized Hamiltonian simulations, observing that our approaches outperform standard ZNE using both small-scale classical simulations and 100-qubit utility-scale experiments on the IBM superconducting hardware. We consider the measurement of both single-site observables as well as two-site correlations along a one-dimensional qubit chain. We also provide a software package for implementing the error mitigation techniques used in this research.
Quantum error mitigation is an important technique to reduce the impact of noise in quantum computers. With more and more qubits being supported on quantum computers, there are two emerging fundamental challenges. First, the number of shots required for quantum algorithms with large numbers of qubits needs to increase in order to obtain a meaningful distribution or expected value of an observable. Second, although steady progress has been made in improving the fidelity of each qubit, circuits with a large number of qubits are likely to produce erroneous results. This low-shot, high-noise regime calls for highly scalable error mitigation techniques. In this paper, we propose a simple and effective mitigation scheme, qubit-wise majority vote, for quantum algorithms with a single correct output. We show that our scheme produces the maximum likelihood (ML) estimate under certain assumptions and bound the number of shots required. Our experimental results on real quantum devices confirm that our proposed approach requires fewer shots than existing ones, and can sometimes recover the correct answers even when they are not observed from the measurement results.
We experimentally study error mitigation and finite-shot sampling on superconducting quantum hardware under a constrained execution budget. The study combines calibration-aware qubit selection, circuit-depth scaling, zero-noise extrapolation, dynamical decoupling, readout-error mitigation, and repeated-shot estimation on an IBM Quantum processor. Experiments are organized across ideal simulation, noise-model simulation, and physical-device execution to separate sampling uncertainty from device-induced error. We investigate how mitigation performance changes with circuit depth, effective noise scale, qubit connectivity, and measurement budget, and quantify accuracy using expectation-value error, mean-squared error, statistical uncertainty, and mitigation gain. A fixed hardware-execution budget is used to evaluate shot allocation strategies and repeated measurements without relying on unlimited sampling. The resulting analysis provides a hardware-aware characterization of when mitigation improves expectation-value estimation and when finite-shot fluctuations offset the benefit of additional mitigation overhead. The implementation uses contemporary Qiskit and IBM Quantum Runtime workflows and is designed to provide reproducible experimental evidence for error-mitigation studies on current quantum processors.
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.
The realization of fault-tolerant quantum computers remains a challenging endeavor, forcing state-of-the-art quantum hardware to rely heavily on noise mitigation techniques. Standard quantum error mitigation is typically based on post-processing strategies. In contrast, the present work explores a pre-processing approach, in which the effects of noise are mitigated before performing a measurement on the output state. The main idea is to find an observable YYY such that its expectation value on a noisy quantum state E(ρ)\mathcal{E(ρ)}E(ρ) matches the expectation value of a target observable XXX on the noiseless quantum state ρρρ. Our method requires the execution of a noisy quantum circuit, followed by the measurement of the surrogate observable YYY. The main enablers of our method in practical scenarios are Tensor Networks. The proposed method improves over Tensor Error Mitigation (TEM) in terms of average error, circuit depth, and complexity, attaining a measurement overhead that approaches the theoretical lower bound. The improvement in terms of classical computation complexity is in the order of ∼106\sim 10^6∼106 times when compared to the post-processing computational cost of TEM in practical scenarios. Such gain comes from eliminating the need to perform the set of informationally complete positive operator-valued measurements (IC-POVM) required by TEM, as well as any other tomographic strategy.
Reducing measurement errors in multiqubit quantum devices is critical for performing any quantum algorithm. Here we show how to mitigate measurement errors by a classical postprocessing of the measured outcomes. Our techniques apply to any experiment where measurement outcomes are used for computing expected values of observables. Two error-mitigation schemes are presented based on tensor product and correlated Markovian noise models. Error rates parametrizing these noise models can be extracted from the measurement calibration data using a simple formula. Error mitigation is achieved by applying the inverse noise matrix to a probability vector that represents the outcomes of a noisy measurement. The error-mitigation overhead, including the number of measurements and the cost of the classical postprocessing, is exponential in $\ensuremath{\epsilon}n$, where $\ensuremath{\epsilon}$ is the maximum error rate and nnn is the number of qubits. We report experimental demonstration of our error-mitigation methods on IBM Quantum devices using stabilizer measurements for graph states with $n\ensuremath{\le}12$ qubits and entangled 20-qubit states generated by low-depth random Clifford circuits.