Biased estimator channels for classical shadows

Journal article : Letter

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 agree with the true mean in expectation. In this Letter, we consider a biased scheme, intentionally introducing a bias in the expectation value by rescaling the conventional classical-shadow estimators to 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 12-qubit spin-ring problem and demonstrate how estimating expected values of nonlocal perturbations can be significantly more efficient using our biased scheme.

Authors: Cai, Z; Chapman, A; Jnane, H; Koczor, B

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: American Physical Society
• Journal: Physical Review A
• Volume: 111
• Issue: 3
• Article number: L030402
• Publication date: 2025-03-21
• Acceptance date: 2025-02-26
• DOI: 10.1103/physreva.111.l030402
• EISSN: 2469-9934
• ISSN: 2469-9926
• Language: English
• Subtype: Letter