Predicting Adaptively Chosen Observables in Quantum Systems
Name
xhn1-vnp9.pdf
Description
Published version
Size
2 MB
Format
Adobe PDF
Checksum (MD5)
8e9c7477777c423f5916e80f415f535c
Author(s)
Huang, Jerry
Lewis, Laura
Huang, Hsin-Yuan
Preskill, John
Date Issued
March 9, 2026
Journal
PRX Quantum
Publisher
American Physical Society (APS)
Version
Final published version
Abstract
Recent advances have demonstrated that 𝒪(log𝑀) measurements suffice to predict 𝑀 properties of arbitrarily large quantum many-body systems. However, these remarkable findings assume that the properties to be predicted are chosen independently of the data. This assumption can be violated in practice, where scientists adaptively select properties after looking at previous predictions. This work investigates the adaptive setting for three classes of observables: local, Pauli, and bounded-Frobenius-norm observables. We prove that Ω(√𝑀) samples of an arbitrarily large unknown quantum state are necessary to predict expectation values of 𝑀 adaptively chosen local and Pauli observables, where the system size scales exponentially and polynomially in 𝑀, respectively. We also present computationally efficient algorithms that achieve this information-theoretic lower bound. In contrast, for bounded-Frobenius-norm observables, we devise an algorithm requiring only 𝒪(log𝑀) samples, independent of system size. These results highlight the potential pitfalls of adaptivity in analyzing data from quantum experiments and provide algorithmic tools to safeguard against erroneous predictions in quantum experiments.
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Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1103/xhn1-vnp9
