Predicting Adaptively Chosen Observables in Quantum Systems
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1.
California Institute of Technology
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2.
Google (United States)
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3.
University of Cambridge
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4.
Massachusetts Institute of Technology
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.
Copyright and License
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Acknowledgement
The authors thank Yu Tong for valuable and inspiring discussions. The authors also thank Ruohan Shen, Haimeng Zhao, Mehdi Soleimanifar, Tai-Hsuan Yang, Yiyi Cai, Charles Cao, Nadine Meister, and Chris Pattison for insightful comments and feedback.
Funding
J.H. is supported by a Caltech Summer Undergraduate Fellowship and a Saul and Joan Cogen Memorial SURF fund. L.L. is supported by a Mellon Mays Undergraduate Fellowship and a Marshall Scholarship. H.H. was supported by a Google PhD fellowship and a MediaTek Research Young Scholarship. H.H. acknowledges the visiting associate position at the Massachusetts Institute of Technology. J.P. acknowledges support from the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research (DE-SC0025535, DE-SC0025572), the U.S. Department of Energy Office of Science, National Quantum Information Science Research Centers, Quantum Systems Accelerator, and the National Science Foundation (PHY-2317110). This work was done (in part) while a subset of the authors visited the Simons Institute for the Theory of Computing. The Institute for Quantum Information and Matter is an NSF Physics Frontiers Center.
Contributions
H.H. and J.P. conceived the project. J.H. led the development of the mathematical proofs with contributions from L.L. and H.H. All authors contributed to the writing of the manuscript.
Data Availability
The data that support the findings of this article are openly available [57].
Files
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Additional details
Related works
- Is new version of
- Discussion Paper: arXiv:2410.15501 (arXiv)
- Is supplemented by
- Dataset: 10.5281/zenodo.18451308 (DOI)
Funding
- Caltech Summer Undergraduate Fellowship
- Saul and Joan Cogen Memorial SURF fund
- Mellon Mays Undergraduate Fellowship
- Marshall Scholarship
- Google PhD fellowship
- MediaTek Research Young Scholarship
- United States Department of Energy
- DE-SC0025535
- United States Department of Energy
- DE-SC0025572
- National Quantum Information Science Research Centers
- Quantum Systems Accelerator
- National Science Foundation
- PHY-2317110
Dates
- Accepted
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2026-01-28
Caltech Custom Metadata
- Caltech groups
- AWS Center for Quantum Computing , Institute for Quantum Information and Matter , Physics Department , Division of Physics, Mathematics and Astronomy (PMA)
- Publication Status
- Published