Learning to Predict Arbitrary Quantum Processes
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1.
California Institute of Technology
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2.
University of California, Berkeley
Abstract
We present an efficient machine-learning (ML) algorithm for predicting any unknown quantum process E over n qubits. For a wide range of distributions D on arbitrary n-qubit states, we show that this ML algorithm can learn to predict any local property of the output from the unknown process E, with a small average error over input states drawn from D. The ML algorithm is computationally efficient even when the unknown process is a quantum circuit with exponentially many gates. Our algorithm combines efficient procedures for learning properties of an unknown state and for learning a low-degree approximation to an unknown observable. The analysis hinges on proving new norm inequalities, including a quantum analogue of the classical Bohnenblust-Hille inequality, which we derive by giving an improved algorithm for optimizing local Hamiltonians. Numerical experiments on predicting quantum dynamics with evolution time up to 106 and system size up to 50 qubits corroborate our proof. Overall, our results highlight the potential for ML models to predict the output of complex quantum dynamics much faster than the time needed to run the process itself.
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 Victor V. Albert, Chi-Fang (Anthony) Chen, Bryan Clark, Richard Kueng, and Spiros Michalakis for valuable input and inspiring discussions. After learning about our proof of the quantum Bohnenblust-Hille inequality, Alexander Volberg and Haonan Zhang found a very different proof with a better Bohnenblust-Hille constant. We thank them for sharing their results with us. H.H. is supported by a Google PhD fellowship. S.C. is supported by NSF Grant No. 2103300. J.P. acknowledges support from the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research (DE-NA0003525, DE-SC0020290), the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Systems Accelerator, and the National Science Foundation (PHY-1733907). The Institute for Quantum Information and Matter is an NSF Physics Frontiers Center.
Funding
H.H. is supported by a Google PhD fellowship. S.C. is supported by NSF Grant No. 2103300. J.P. acknowledges support from the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research (DE-NA0003525, DE-SC0020290), the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Systems Accelerator, and the National Science Foundation (PHY-1733907). The Institute for Quantum Information and Matter is an NSF Physics Frontiers Center.
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Additional details
Related works
- Is new version of
- Discussion Paper: arXiv:2210.14894 (arXiv)
Funding
- Google (United States)
- Google PhD fellowship
- National Science Foundation
- DMS-2103300
- United States Department of Energy
- DE-NA0003525
- United States Department of Energy
- DE-SC0020290
- National Science Foundation
- PHY-1733907
Dates
- Accepted
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2023-11-15Accepted