{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T18:12:44Z","timestamp":1777486364844,"version":"3.51.4"},"reference-count":43,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T00:00:00Z","timestamp":1763078400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science Foundation","award":["DMS-2111221"],"award-info":[{"award-number":["DMS-2111221"]}]},{"name":"National Science Foundation","award":["CCF- 2312456"],"award-info":[{"award-number":["CCF- 2312456"]}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"\n 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\n \n &#x03B5;<\/mml:mi>\n <\/mml:math>\n , 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.\n <\/jats:p>","DOI":"10.22331\/q-2025-11-14-1909","type":"journal-article","created":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T13:04:01Z","timestamp":1763125441000},"page":"1909","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":3,"title":["Direct Analysis of Zero-Noise Extrapolation: Polynomial Methods, Error Bounds, and Simultaneous Physical-Algorithmic Error Mitigation"],"prefix":"10.22331","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-0227-1310","authenticated-orcid":false,"given":"Pegah","family":"Mohammadipour","sequence":"first","affiliation":[{"name":"Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9760-7292","authenticated-orcid":false,"given":"Xiantao","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2025,11,14]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"John Preskill. ``Quantum computing in the nisq era and beyond''. 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