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.
Luciano Pereira de Souza (Tue,) studied this question.