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arXiv:2402.04000 · Physical Review A

Quantum error mitigation by layerwise Richardson extrapolation

Vincent Russo, Andrea Mari

Published Dec 17, 2024• 6 citations
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Abstract

The authors present an error-mitigation scheme in which the noise from different layers of a quantum circuit can be amplified and then extrapolated to the zero-noise limit independently. In doing this they enhance the traditional Richardson extrapolation protocol with the flexibility of layerwise unitary folding schemes.
DOI
10.1103/physreva.110.062420

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We investigate a hybrid quantum-classical approach to quantum error mitigation. We propose Classically Augmented Zero-Noise Extrapolation, a hybrid error-mitigation method in which high-noise Richardson extrapolation nodes are replaced by classically simulated estimates. These classical nodes have negligible sampling variance but introduce deterministic simulation bias. We derive the resulting variance reduction under optimal shot allocation and show that, for linear node spacings and fixed index cutoff, the coefficient-level reduction can be exponential. We validate the prediction numerically using Pauli-propagation simulations and demonstrate a reduction in mean-squared error when the truncation bias is sufficiently small.
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Abstract Quantum error mitigation is a key enabling technique for extracting reliable computational results from noisy intermediate-scale quantum devices. Among existing approaches, zero-noise extrapolation (ZNE) is widely employed, but its effectiveness deteriorates in high-noise regimes or deep circuits, where measurement outcomes converge to the random-guessing limit. To address this issue, we propose a lightweight, extrapolation-based error mitigation framework that leverages the intrinsic repetitive structure of quantum algorithms. We classify these algorithms into homogeneous and heterogeneous types and efficiently estimate block fidelities using shallow identity sequences of the core operational block, thereby avoiding global circuit folding. Experiments on IBM’s advanced superconducting platform and its corresponding simulator demonstrate that the proposed framework remains effective even in high-noise regimes where folding-based ZNE(f-ZNE) fails due to noise saturation. For a four-qubit Grover search, our approach restores the success probability to near its theoretical value, whereas f-ZNE yields negligible improvement. We further validate the proposed method on a 17-qubit quantum approximate optimization algorithm with layer-dependent parameters, demonstrating robustness beyond fixed-structure circuits. These results indicate that leveraging algorithmic structure provides a practical pathway to extending the performance of extrapolation-based error mitigation on current quantum processors.
Quantum computers in the NISQ era are prone to noise. A range of quantum error mitigation techniques has been proposed to address this issue. Zero-noise extrapolation (ZNE) stands out as a promising one. ZNE involves increasing the noise levels in a circuit and then using extrapolation to infer the zero noise case from the noisy results obtained. This paper presents a novel ZNE approach that does not require circuit folding or noise scaling to mitigate depolarizing and/or decoherence noise. To mitigate depolarizing noise, we propose leveraging the extreme/infinite noisy case, which allows us to avoid circuit folding. Specifically, the circuit output with extreme noise becomes the maximally mixed state. We show that using circuit-reliability metrics, simple linear extrapolation can effectively mitigate depolarizing noise. With decoherence noise, different states decay into the all-zero state at a rate that depends on the number of excited states and time. Therefore, we propose a state- and latency-aware exponential extrapolation that does not involve folding or scaling. When dealing with a quantum system affected by both decoherence and depolarizing noise, we propose to use our two mitigation techniques in sequence: first applying decoherence error mitigation, followed by depolarizing error mitigation. A common limitation of ZNE schemes is that if the circuit of interest suffers from high noise, scaling-up noise levels could not provide useful data for extrapolation. We propose using circuit-cut techniques to break a large quantum circuit into smaller sub-circuits to overcome this limitation. This way, the noise levels of the sub-circuits are lower than the original circuit, and ZNE can become more effective in mitigating their noises.