Out-of-distribution generalization for learning quantum dynamics

ORAL

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.

*MCC 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), and by the BMWi (PlanQK). NE was supported by the U.S. DOE, Department of Energy Computational Science Graduate Fellowship under Award Number DE-SC0020347. HH 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. Research presented in this paper (ATS) was supported by the Laboratory Directed Research and Development (LDRD) program of Los Alamos National Laboratory under project number 20210116DR. LC acknowledges support from LDRD program of LANL under project number 20200022DR. LC and PJC 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. ZH acknowledges support from the LANL Mark Kac Fellowship.

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Publication: Matthias C. Caro, Hsin-Yuan Huang, Nicholas Ezzell, Joe Gibbs, Andrew T. Sornborger, Lukasz Cincio, Patrick J. Coles, and Zoë Holmes. Out-of-distribution generalization for learning quantum dynamics. Version 1. Apr. 21, 2022. arXiv: 2204.10268 [quant-ph].
Manuscript submitted for publication.

Presenters

  • Matthias C Caro

    • California Institute of Technology

Authors

  • Matthias C Caro

    • California Institute of Technology

  • Hsin-Yuan Huang

    • Caltech

  • Nic Ezzell

    • University of Southern California

  • Joe Gibbs

    • AWE
    • Atomic Weapons Establishment

  • Andrew T Sornborger

    • Los Alamos National Laboratory

  • Lukasz Cincio

    • Los Alamos National Laboratory
    • Los Alamos National Lab

  • Patrick J Coles

    • Los Alamos National Laboratory

  • Zoe Holmes

    • Los Alamos National Laboratory
    • École polytechnique fédérale de Lausanne