Out-of-distribution generalization for learning quantum dynamics

Creators: Caro, Matthias C.; Huang, Hsin-Yuan; Ezzell, Nicholas; Gibbs, Joe; Sornborger, Andrew T.; Cincio, Lukasz; Coles, Patrick J.; Holmes, Zoë

Abstract

Generalization bounds are a critical tool to assess the training data requirements of Quantum Machine Learning (QML). Recent work has established guarantees for in-distribution generalization of quantum neural networks (QNNs), where training and testing data are drawn from the same data distribution. However, there are currently no results on out-of-distribution generalization in QML, where we require a trained model to perform well even on data drawn from a different distribution to the training distribution. Here, we prove out-of-distribution generalization for the task of learning an unknown unitary. In particular, we show that one can learn the action of a unitary on entangled states having trained only product states. Since product states can be prepared using only single-qubit gates, this advances the prospects of learning quantum dynamics on near term quantum hardware, and further opens up new methods for both the classical and quantum compilation of quantum circuits.

Additional Information

© The Author(s) 2023. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. We thank Marco Cerezo for helpful conversations. We thank the reviewers at Nature Communications for their valuable feedback. 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. N.E. was supported by the U.S. DOE, Department of Energy Computational Science Graduate Fellowship under Award Number DE-SC0020347. H.-Y.H. is supported by a Google PhD Fellowship. P.J.C. and A.T.S. acknowledge initial support from the Los Alamos National Laboratory (LANL) ASC Beyond Moore's Law project. Research presented in this paper (A.T.S.) was supported by the Laboratory Directed Research and Development (LDRD) program of Los Alamos National Laboratory under project number 20210116DR. L.C. acknowledges support from LDRD program of LANL under project number 20230049DR. 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 Accelerated Research in Quantum Computing (ARQC) program. Z.H. acknowledges support from the LANL Mark Kac Fellowship and from the Sandoz Family Foundation-Monique de Meuron program for Academic Promotion. Data availability: The data generated and analyzed during the current study are available from the authors upon request. Code availability: Further implementation details are available from the authors upon request. Contributions: The project was conceived by M.C.C., H.-Y.H., A.T.S., L.C., P.J.C., and Z.H. Theoretical results were proved by M.C.C., H.-Y.H., and Z.H. Numerical implementations were performed by N.E., J.G., and L.C. The manuscript was written by M.C.C., H.-Y.H., N.E., J.G., A.T.S., L.C., P.J.C., and Z.H. The authors declare no competing interests.

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