Learning Conservation Laws in Unknown Quantum Dynamics
Abstract
We present a learning algorithm for discovering conservation laws given as sums of geometrically local observables in quantum dynamics. This includes conserved quantities that arise from local and global symmetries in closed and open quantum many-body systems. The algorithm combines the classical shadow formalism for estimating expectation values of observable and data analysis techniques based on singular value decompositions and robust polynomial interpolation to discover all such conservation laws in unknown quantum dynamics with rigorous performance guarantees. Our method can be directly realized in quantum experiments, which we illustrate with numerical simulations, using closed and open quantum system dynamics in a ℤ₂ gauge theory and in many-body localized spin chains.
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
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PRXQuantum.5.010350.pdf
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Additional details
Funding
- United States Department of Energy
- DE-NA0003525
- United States Department of Energy
- DE-SC0020290
- United States Department of Energy
- DE-SC0019374
- United States Department of Energy
- DE-SC0020290
- California Institute of Technology
- Institute for Quantum Information and Matter
- National Science Foundation
- PHY-2210452
- German National Academy of Sciences Leopoldina
- LPDS 2021-02
- California Institute of Technology
- Walter Burke Institute for Theoretical Physics