Biased Estimator Channels for Classical Shadows
arXiv:2402.09511 · doi:10.1103/PhysRevA.111.L030402
Abstract
Extracting classical information from quantum systems is of fundamental importance, and classical shadows allow us to extract a large amount of information using relatively few measurements. Conventional shadow estimators are unbiased and thus approach the true mean in the infinite-sample limit. In this work, we consider a biased scheme, intentionally introducing a bias by rescaling the conventional classical shadows estimators can reduce the error in the finite-sample regime. The approach is straightforward to implement and requires no quantum resources. We analytically prove average case as well as worst- and best-case scenarios, and rigorously prove that it is, in principle, always worth biasing the estimators. We illustrate our approach in a quantum simulation task of a -qubit spin-ring problem and demonstrate how estimating expected values of non-local perturbations can be significantly more efficient using our biased scheme.
13 pages, 5 figures
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