Direct Analysis of Zero-Noise Extrapolation: Polynomial Methods, Error Bounds, and Simultaneous Physical-Algorithmic Error Mitigation

• URL: http://arxiv.org/abs/2502.20673v2
• Date: Wed, 19 Mar 2025 23:54:28 GMT
• Title: Direct Analysis of Zero-Noise Extrapolation: Polynomial Methods, Error Bounds, and Simultaneous Physical-Algorithmic Error Mitigation
• Authors: Pegah Mohammadipour, Xiantao Li,
• Abstract summary: Zero-noise extrapolation (ZNE) is a widely used quantum error mitigation technique that artificially amplifies circuit noise and extrapolates the results to the noise-free circuit.<n>This paper provides a comprehensive analysis of these challenges, presenting bias and variance that quantify errors.<n>We propose a strategy for simultaneously mitigating circuit and algorithmic errors by jointly scaling the time step size and the noise level.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $\varepsilon$, 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.

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