Learning Conservation Laws in Unknown Quantum Dynamics

Creators: Zhan, Yongtao; Elben, Andreas; Huang, Hsin-Yuan; Tong, Yu

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

The authors thank the inspiring discussions with John Preskill, Elmer V. H. Doggen, Laimei Nie, Pablo Sala, and Benoit Vermersch. Y.T. acknowledges funding from the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, (DE-NA0003525, and DE-SC0020290), and from the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under Award No. DE-SC0019374. Work supported by DE-SC0020290 is supported by the DOE QuantISED program through the theory consortium “Intersections of QIS and Theoretical Particle Physics” at Fermilab. The Institute for Quantum Information and Matter at Caltech is an NSF Physics Frontiers Center. The work of A.E. was performed in part at the Aspen Center for Physics, which is supported by the National Science Foundation under Grant No. PHY-2210452. Furthermore, A.E. acknowledges funding from the German National Academy of Sciences Leopoldina under Grant No. LPDS 2021-02 and from the Walter Burke Institute for Theoretical Physics at Caltech.

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