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arXiv:2307.05203 · IEEE International Conference on Quantum Computing and Engineering (QCE)

Best Practices for Quantum Error Mitigation with Digital Zero-Noise Extrapolation

Ritajit Majumdar, Pedro Rivero, Friederike Metz, Areeq Hasan, Derek S. Wang

Published Sep 17, 2023• 26 citations
arXivHTMLPDF

Abstract

Digital zero-noise extrapolation (dZNE) has emerged as a common approach for quantum error mitigation (QEM) due to its conceptual simplicity, accessibility, and resource efficiency. In practice, however, properly applying dZNE to extend the computational reach of noisy quantum processors is rife with subtleties. Here, based on literature review and original experiments on noisy simulators and real quantum hardware, we define best practices for QEM with dZNE for each step of the workflow, including noise amplification, execution on the quantum device, extrapolation to the zero-noise limit, and composition with other QEM methods. We anticipate that this effort to establish best practices for dZNE will be extended to other QEM methods, leading to more reproducible and rigorous calculations on noisy quantum hardware. The full version of this paper can be found in Ref. [1].

DOI
10.1109/qce57702.2023.00102

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•Dec 8, 2025•1 citation
Digital zero-noise extrapolation (dZNE) has emerged as a common approach for quantum error mitigation (QEM) due to its conceptual simplicity, accessibility, and resource efficiency. In practice, however, properly applying dZNE to extend the computational reach of noisy quantum processors is rife with subtleties. Here, based on literature review and original experiments on noisy simulators and real quantum hardware, we define best practices for QEM with dZNE for each step of the workflow, including noise amplification, execution on the quantum device, extrapolation to the zero-noise limit, and composition with other QEM methods. We anticipate that this effort to establish best practices for dZNE will be extended to other QEM methods, leading to more reproducible and rigorous calculations on noisy quantum hardware. The full version of this paper can be found in Ref. [1].
Zero-noise extrapolation (ZNE) is an increasingly popular technique for mitigating errors in noisy quantum computations without using additional quantum resources. We review the fundamentals of ZNE and propose several improvements to noise scaling and extrapolation, the two key components in the technique. We introduce unitary folding and parameterized noise scaling. These are digital noise scaling frameworks, i.e. one can apply them using only gate-level access common to most quantum instruction sets. We also study different extrapolation methods, including a new adaptive protocol that uses a statistical inference framework. Benchmarks of our techniques show error reductions of 18X to 24X over non-mitigated circuits and demonstrate ZNE's effectiveness at larger qubit numbers than have been tested previously. In addition to presenting new results, this work is a self-contained introduction to the practical use of ZNE by quantum programmers.
As an alternative to quantum error correction, quantum error mitigation methods, including Zero-Noise Extrapolation (ZNE), have been proposed to alleviate run-time errors in current noisy quantum devices. In this work, we propose a modified version of ZNE that provides for a significant performance enhancement on current noisy devices. Our modified ZNE method extrapolates to zero-noise data by evaluating groups of noisy data obtained from noise-scaled circuits and selecting extrapolation functions for each group with the assistance of estimated noisy simulation results. To quantify enhancement in a real-world quantum application, we embed our modified ZNE in Quantum Random Access Memory (QRAM) - a memory system important for future quantum networks and computers. Our new ZNE-enhanced QRAM designs are experimentally implemented on a 27-qubit noisy superconducting quantum device, the results of which demonstrate QRAM fidelity can be improved significantly relative to traditional ZNE usage. Our results demonstrate the critical role the extrapolation function plays in ZNE - judicious choice of that function on a per-measurement basis can make the difference between a quantum application being functional or non-functional.
The pursuit of practical quantum utility on near-term quantum processors is critically challenged by their inherent noise. Quantum error mitigation (QEM) techniques are leading solutions to improve computation fidelity with relatively low qubit-overhead, while full-scale quantum error correction remains a distant goal. However, QEM techniques incur substantial measurement overheads, especially when applied to families of quantum circuits parameterized by classical inputs. Focusing on zero-noise extrapolation (ZNE), a widely adopted QEM technique, here we devise the surrogate-enabled ZNE (S-ZNE), which leverages classical learning surrogates to perform ZNE entirely on the classical side. Unlike conventional ZNE, whose measurement cost scales linearly with the number of circuits, S-ZNE requires only constant measurement overhead for an entire family of quantum circuits, offering superior scalability. Theoretical analysis indicates that S-ZNE achieves accuracy comparable to conventional ZNE in many practical scenarios, and numerical experiments on up to 100-qubit ground-state energy and quantum metrology tasks confirm its effectiveness. Our approach provides a template that can be effectively extended to other quantum error mitigation protocols, opening a promising path toward scalable error mitigation.
Zero-noise extrapolation (ZNE) is a widely used quantum error mitigation technique that artificially amplifies circuit noise and then extrapolates the results to the noise-free circuit. A common ZNE approach is Richardson extrapolation, which relies on polynomial interpolation. Despite its simplicity, efficient implementations of Richardson extrapolation face several challenges, including approximation errors from the non-polynomial behavior of noise channels, overfitting due to polynomial interpolation, and exponentially amplified measurement noise. This paper provides a comprehensive analysis of these challenges, presenting bias and variance bounds that quantify approximation errors. Additionally, for any precision ε , our results offer an estimate of the necessary sample complexity. We further extend the analysis to polynomial least squares-based extrapolation, which mitigates measurement noise and avoids overfitting. Finally, we propose a strategy for simultaneously mitigating circuit and algorithmic errors in the Trotter-Suzuki algorithm by jointly scaling the time step size and the noise level. This strategy provides a practical tool to enhance the reliability of near-term quantum computations. We support our theoretical findings with numerical experiments.
Reliable benchmarking of Quantum Error Mitigation (QEM) requires distinguishing genuine improvements from artefacts of the post-processing arithmetic. In this paper, we expose a failure mode in Richardson Zero-Noise Extrapolation (ZNE), a widely used technique routinely (and often implicitly) relied upon in benchmarks and experiments. When noise amplification operates beyond usable signals - a regime that is quickly reached on current hardware for non-trivial circuits - we show that the extrapolation no longer reflects the underlying physics, but collapses into a fixed rescaling of a single noisy measurement, producing a bogus apparent improvement that is independent of noise amplification. This poses a rarely considered threat to the validity of many empirical evaluations in quantum computing. Measurements on real hardware (IQM Euro-Q-Exa) confirm this collapse with ordinary folding alone: as circuit depth erodes the signal, the reported estimate decouples from the truth and overshoots the ideal by up to 21%. We further introduce a matched-cost "garbage-folding" negative control that carries no usable signal yet reports a larger apparent improvement than genuine folding - showing that the magnitude of an improvement is not evidence of its correctness - alongside a zero-cost check flagging the artefact from data a benchmark already holds. We distil both into a short reporting checklist for ZNE benchmarks.
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.