Variance reduction methods in the estimation of Pauli sums

Quantum Physics [Submitted on 20 Mar 2026] Variance reduction methods in the estimation of Pauli sums Søren Fuglede Jørgensen, Rafael Emilio Barfknecht, Patrick Ettenhuber, Nikolaj Thomas Zinner Accurately estimating expectation values of quantum observables with as few measurements as possible is crucial to many quantum computing applications. We introduce a framework that covers many of existing measurement strategies and introduce heuristics that can be used to enhance randomized schemes, including those based on Pauli grouping with inverse probability weighting and variants of the classical shadow algorithm. We show how to maximize information gain from such schemes, while carefully optimizing the distribution of possible measurements, and show that simple grouping algorithms can get close to, and in some cases exceed, state-of-the-art accuracy for unbiased estimation of expectation values on a standard quantum chemistry benchmark. We show how these randomized methods may be compared to more recent measurement schemes, such as shadow grouping, derandomized shadow, and overlapped grouping measurement, we show how the same strategies can be used to augment these schemes, and we demonstrate that we can reduce measurement costs by up to a factor of two by allowing Clifford measurement circuits for otherwise Clifford-less methods. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.20029 [quant-ph]   (or arXiv:2603.20029v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.20029 Focus to learn more Submission history From: Søren Fuglede Jørgensen [view email] [v1] Fri, 20 Mar 2026 15:16:45 UTC (1,233 KB) Access Paper: view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)