The Noisy Intermediate-Scale Quantum (NISQ) era is characterized by high error rates that fundamentally limit the utility of quantum algorithms. Existing error mitigation techniques—Zero-Noise Extrapolation (ZNE), Probabilistic Error Cancellation (PEC), and Clifford Data Regression (CDR)—achieve varying degrees of success but lack a unified signal-processing perspective. Motivated by the recently established isomorphism between Kraus operator representations and discrete impulse decompositions in digital signal processing (DSP), we present a novel quantum error mitigation framework that treats noisy quantum channels as linear time-invariant systems amenable to deconvolution. We adapt classical Wiener filtering theory to the quantum domain via the Liouville superoperator representation, formulating error mitigation as a linear minimum mean-square error (LMMSE) estimation problem in the space of density operators. Experimental validation across five representative NISQ scenarios demonstrates that the Quantum Wiener Filter (QWF) significantly outperforms ZNE, PEC, and CDR in four of five test cases, achieving 66–93% reduction in observable error for GHZ state preparation under amplitude damping, VQE energy estimation under thermal relaxation, random Clifford circuits under depolarizing noise, and QAOA optimization under crosstalk. The method exhibits statistically significant superiority (Wilcoxon signed-rank test, p < 10⁻⁴) across 30 independent trials per scenario. The fifth scenario—an adversarial state-dependent noise model—validates the Markovian assumption underlying the deconvolution framework by demonstrating controlled failure when channel linearity is violated. Our results establish that the DSP-QM isomorphism enables practical error mitigation with superior fidelity recovery (mean fidelity 0.96–0.99 vs. 0.78–0.98 for baselines) at modest computational overhead (1.2× shot budget). This work bridges quantum information theory and classical signal processing, opening a new avenue for NISQ algorithm optimization.Keywords: Quantum Error Mitigation, NISQ, Wiener Filter, Signal Processing, Qiskit.
The Noisy Intermediate-Scale Quantum (NISQ) era is characterized by high error rates that fundamentally limit the utility of quantum algorithms. Existing error mitigation techniques—Zero-Noise Extrapolation (ZNE), Probabilistic Error Cancellation (PEC), and Clifford Data Regression (CDR)—achieve varying degrees of success but lack a unified signal-processing perspective. Motivated by the recently established isomorphism between Kraus operator representations and discrete impulse decompositions in digital signal processing (DSP), we present a novel quantum error mitigation framework that treats noisy quantum channels as linear time-invariant systems amenable to deconvolution. We adapt classical Wiener filtering theory to the quantum domain via the Liouville superoperator representation, formulating error mitigation as a linear minimum mean-square error (LMMSE) estimation problem in the space of density operators. Experimental validation across five representative NISQ scenarios demonstrates that the Quantum Wiener Filter (QWF) significantly outperforms ZNE, PEC, and CDR in four of five test cases, achieving 66–93% reduction in observable error for GHZ state preparation under amplitude damping, VQE energy estimation under thermal relaxation, random Clifford circuits under depolarizing noise, and QAOA optimization under crosstalk. The method exhibits statistically significant superiority (Wilcoxon signed-rank test, p < 10⁻⁴) across 30 independent trials per scenario. The fifth scenario—an adversarial state-dependent noise model—validates the Markovian assumption underlying the deconvolution framework by demonstrating controlled failure when channel linearity is violated. Our results establish that the DSP-QM isomorphism enables practical error mitigation with superior fidelity recovery (mean fidelity 0.96–0.99 vs. 0.78–0.98 for baselines) at modest computational overhead (1.2× shot budget). This work bridges quantum information theory and classical signal processing, opening a new avenue for NISQ algorithm optimization.Keywords: Quantum Error Mitigation, NISQ, Wiener Filter, Signal Processing, Qiskit.
Quantum error mitigation (QEM) bridges the gap between today's noisy NISQ hardware and fault-tolerant quantum computing by reducing the effect of hardware errors on expectation value estimates without the qubit overhead of full quantum error correction. This paper proposes the Quantum Error Mitigation Design (QEMD) framework, a systematic evaluation of six QEM techniques across four circuit families on IBM Quantum Eagle and IonQ Forte: Zero-Noise Extrapolation (ZNE), Probabilistic Error Cancellation (PEC), Clifford Data Regression (CDR), Symmetry Verification (SV), Dynamical Decoupling (DD), and a novel Adaptive Ensemble Mitigation (AEM) combining ZNE and CDR with context-aware technique selection. QEMD finds: ZNE 3-point Richardson provides the best cost-performance trade-off for QAOA and VQE circuits (4.8x overhead, 28.4pp error reduction); PEC provides the highest accuracy but at 48x shot overhead -- practical only for n <= 12; DD reduces coherence-limited errors by 18.4% on IonQ Forte at zero shot overhead; AEM outperforms all individual techniques by 6.4pp at 8.4x overhead. QEMD provides a decision guide mapping circuit type, qubit count, and shot budget to optimal QEM technique selection.
The paper presents a comprehensive review of current error mitigation strategies within quantum neural networks operating in the NISQ era. The research models complex hardware noise environments using Qiskit Aer simulators to evaluate various error compensation algorithms. Specifically, the study investigates how global depolarizing channels fundamentally flatten the optimization landscape and artificially exacerbate the barren plateaus phenomenon, effectively preventing the convergence of gradient-based optimizers. To address these hardware limitations, the study tests the efficiency of Zero-Noise Extrapolation (ZNE), Probabilistic Error Cancellation (PEC), Readout Error Mitigation (REM), and Clifford Data Regression (CDR). The empirical analysis demonstrates that quantum error mitigation techniques successfully restore the true direction of the gradient vector by compensating for the amplitude attenuation caused by decoherence. Consequently, the optimization process strictly requires an exponential or linear increase in the number of measurement shots to compensate for the heavily inflated statistical variance introduced by the mitigation models. The investigation identifies REM as a mandatory baseline classical processing step that corrects asymmetric measurement biases without incurring additional quantum sampling costs. Simultaneously, the study restricts the practical utility of ZNE to shallow quantum circuits to prevent the accumulation of severe extrapolation inaccuracies, which otherwise cause destabilizing oscillations during the late epochs of gradient descent. Furthermore, the analysis proves that while PEC supplies mathematically unbiased gradient estimators, its exponential sampling overhead renders it intractable for deep parameterized architectures. Moreover, the experiments reveal a complex trade-off between optimization accuracy and computational overhead on the quantum coprocessor, highlighting CDR as a highly scalable alternative that shifts the mitigation burden to classical pre-processing. As a result, the authors propose a dynamic orchestration methodology that strategically combines ZNE, CDR and PEC mitigation strategies throughout the training cycle to ensure stable gradient descent convergence while minimizing resource consumption. The findings provide a robust theoretical foundation for designing resilient hybrid quantum-classical machine learning architectures and integrating them into modern MLOps pipelines.
Abstract The practical application of Noisy Intermediate-Scale Quantum (NISQ) hardware is fundamentally limited by gate-level noise, which corrupts computational results. This research addresses this challenge through the development and validation of a modular software framework for Quantum Error Mitigation (QEM). We implement and compare two leading QEM strategies: Zero-Noise Extrapolation (ZNE) and Probabilistic Error Cancellation (PEC). The framework is built using the Qiskit library and is validated using a realistic, hardware-calibrated noisy simulator that mimics the error characteristics of a real IBM Quantum device. Our methodology focuses on a robust implementation of ZNE via unitary folding and a proof-of-concept demonstration of the PEC algorithm. The framework's effectiveness is demonstrated on a simulated noisy backend where, for a 3-qubit Greenberger-Horne-Zeilinger (GHZ) state, the baseline state fidelity was increased from 93.5% to 97.3% via ZNE, corresponding to a 59% reduction in the state's infidelity. This work provides a practical demonstration of how software-based error mitigation can enhance the reliability of quantum computations on current noisy hardware.
Abstract Quantum computing has recently emerged as a novel paradigm for solving problems otherwise intractable on classical computers, yet the practical progress of quantum computers is severely impacted by noise, decoherence, and imperfect gate operations in Noisy Intermediate-Scale Quantum (NISQ) devices. Specific to IBM Quantum hardware, imperfections due to readout error, gate errors, and device drift, which depends on time, resolves limits for the accuracy of outputs from our algorithms. The mitigation strategies currently used, for example, Measurement Error Mitigation (MEM), Zero Noise Extrapolation (ZNE), and Clifford Data Regression (CDR), offer improvement over raw, unmitigated outputs, but they are static and not dynamic; the reduction of noise in within an NISQ device is temporal and can vary in patterns that are non-zero. In addition to this, using the conventional methods provides inconsistent and suboptimal results.This study will provide enhanced reliability with respect to performing quantum computation on IBM Quantum hardware with a unique mitigation framework that is adaptive and computationally efficient for a high-fidelity output. The problem taken on here is the failure of existing error mitigation strategies to provide adaptive noise compensation, as they assume a statically-distributed error, despite the performance-related characteristics already being documented in regards to calibration drift and variation over time.To achieve this, we propose a Hybrid Adaptive Error Mitigation (HAEM) approach that includes baseline measurement error mitigation and an additional correction layer that utilizes realtime calibration information, along with lightweight machine learning models. The approach can be broken down into three steps: (i) perform standard measurement error mitigation to reduce classical readout noise, (ii) execute compact calibration circuits, such as Bell states, GHZ states and Clifford benchmarks to capture then current error profile of the device, and (iii) use a lightweight machine learning model (having been trained on historical and newest calibration data) to dynamically change the mitigation weights applied for the target quantum algorithm. All implementation is done using Qiskit Runtime to ensure low-latency execution, and we completed experiments on both Qiskit Aer noisy simulators and IBM Quantum devices.Initial results suggest HAEM improved the outputs of quantum algorithms' fidelity compared to the unmitigated runs and the baseline measurement error mitigation (MEM) runs. On the noisy simulators, HAEM increased fidelity from a raw performance of 0.65 to 0.87, nearly a 34% improvement. In fairer hardware-like scenarios, fidelity-on-average was persistently 12% better than MEM, with nearly equal time duration for the additional adaptive measurements. The adaptive aspect of HAEM consistently supported subsequent calibration cycles of the device and was effective to continue providing fidelity improvements despite the static mitigation performance degrading.To sum up, the proposed HAEM framework is a modern and viable alternative for error mitigation which brings together the benefits of baseline approaches with corrections that are driven by fixed-function error-corrective, adaptive learning. As both learning-based and standard baseline approaches can only achieve fixed levels of performance, HAEM, through its use of noise mitigation both at execution time and through correlating it with standard data, provides a route towards reliable quantum computations on current IBM hardware. HAEM also presents a contribution to the NISQ error-resilient landscape, and however it is intended that it will continue to improve future applications of hybrid workflows of quantum and classical computation where error mitigation and resilience is important.
Quantum Neural Networks (QNNs) represent a promising direction within Quantum Machine Learning (QML), yet their realization on noisy intermediate-scale quantum (NISQ) devices remains constrained by decoherence, gate imperfections, crosstalk, and readout errors. This study provides a systematic evaluation of noise effects and mitigation strategies in hybrid quantum neural networks (HQNNs). Zero-Noise Extrapolation (ZNE), Digital Dynamical Decoupling (DDD), and Layerwise Richardson Extrapolation (LRE) are incorporated into end-to-end QNN training pipelines developed with PennyLane, simulated using Qiskit Aer noise models, and integrated with the Mitiq framework, while Probabilistic Error Cancellation (PEC) is evaluated separately under depolarizing noise due to its computational cost. Experiments conducted on the Iris dataset with five representative noise channels show that the impact of noise and the effect of mitigation are strongly dependent on the noise model and its strength. The model maintains comparatively strong performance under phase-flip and phase-damping noise, while substantial degradation is observed under high depolarizing and amplitude-damping noise. Across the evaluated mitigation methods, the observed benefits remain limited and noise-dependent: ZNE, DDD, and LRE generally follow the same degradation trends as the unmitigated baseline, while PEC shows limited gains only in the low-noise depolarizing regime. These findings highlight the need for context-specific mitigation strategies to improve the robustness of QNNs in practical NISQ settings.
We propose a general framework for quantum error mitigation that combines and generalizes two techniques: probabilistic error cancellation (PEC) and zero-noise extrapolation (ZNE). Similar to PEC, the proposed method represents ideal operations as linear combinations of noisy operations that are implementable on hardware. However, instead of assuming a fixed level of hardware noise, we extend the set of implementable operations by noise scaling. By construction, this method encompasses both PEC and ZNE as particular cases and allows us to investigate a larger set of hybrid techniques. For example, gate extrapolation can be used to implement PEC without requiring knowledge of the device's noise model, e.g., avoiding gate-set tomography. Alternatively, probabilistic error reduction can be used to estimate expectation values at intermediate virtual noise strengths (below the hardware level), leading to partially mitigated results at a lower sampling cost. Moreover, multiple results obtained with different noise-reduction factors can be further postprocessed with ZNE to better approximate the zero-noise limit.