Dynamical simulation via quantum machine learning with provable generalization
Abstract
Much attention has been paid to dynamical simulation and quantum machine learning (QML) independently as applications for quantum advantage, while the possibility of using QML to enhance dynamical simulations has not been thoroughly investigated. Here we develop a framework for using QML methods to simulate quantum dynamics on near-term quantum hardware. We use generalization bounds, which bound the error a machine learning model makes on unseen data, to rigorously analyze the training data requirements of an algorithm within this framework. Our algorithm is thus resource efficient in terms of qubit and data requirements. Furthermore, our preliminary numerics for the XY model exhibit efficient scaling with problem size, and we simulate 20 times longer than Trotterization on IBMQ-Bogota.
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
We thank Sujay Kazi, Elliott Ball, and Robert M. Parrish for helpful conversations. Z.H. acknowledges support from the LANL Mark Kac Fellowship and from the Sandoz Family Foundation-Monique de Meuron program for Academic Promotion. M.C.C. was supported by the TopMath Graduate Center of the TUM Graduate School at the Technical University of Munich, Germany, the TopMath Program at the Elite Network of Bavaria, by a doctoral scholarship of the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes), by the BMWK (PlanQK), and by a DAAD PRIME Fellowship. NE was supported by the U.S. DOE, Department of Energy Computational Science Graduate Fellowship under Award No. DE-SC0020347. H.H. is supported by a Google PhD Fellowship. PJC and ATS acknowledge initial support from the Los Alamos National Laboratory (LANL) ASC Beyond Moore's Law project. ATS was also supported by the Laboratory Directed Research and Development (LDRD) program of Los Alamos National Laboratory under Project No. 20210116DR. L.C. acknowledges support from LDRD program of LANL under Project No. 20200022DR. L.C. and P.J.C. were also supported by the U.S. DOE, Office of Science, Office of Advanced Scientific Computing Research, under the Quantum Computing Application Teams (QCAT) program.
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Additional details
- Los Alamos National Laboratory
- Mark Kac Fellowship
- Technical University of Munich
- German National Academic Foundation
- Federal Ministry for Economic Affairs and Climate Action
- German Academic Exchange Service
- United States Department of Energy
- DOE Computational Science Graduate Fellowship DE-SC0020347
- Google (United States)
- Google PhD Fellowship
- Los Alamos National Laboratory
- 20210116DR
- Los Alamos National Laboratory
- 20200022DR
- Caltech groups
- Institute for Quantum Information and Matter