Out-of-distribution generalization for learning quantum dynamics

Matthias C. Caro (), Hsin-Yuan Huang, Nicholas Ezzell, Joe Gibbs, Andrew T. Sornborger, Lukasz Cincio, Patrick J. Coles and Zoë Holmes
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Matthias C. Caro: Technical University of Munich
Hsin-Yuan Huang: Caltech
Nicholas Ezzell: Los Alamos National Laboratory
Joe Gibbs: University of Surrey
Andrew T. Sornborger: Los Alamos National Laboratory
Lukasz Cincio: Los Alamos National Laboratory
Patrick J. Coles: Los Alamos National Laboratory
Zoë Holmes: Los Alamos National Laboratory

Nature Communications, 2023, vol. 14, issue 1, 1-9

Abstract: 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.

Date: 2023
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DOI: 10.1038/s41467-023-39381-w

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