Out-of-distribution generalization for learning quantum dynamics

Journal Article · 04 July 2023 · Nature Communications

DOI: https://doi.org/10.1038/s41467-023-39381-w · OSTI ID:1988191

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.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE; USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: 89233218CNA000001
• OSTI ID: 1988191
• Report Number(s): LA-UR--22-23623; LA-UR--23-26072; 3751; PII: 39381
• Journal Information: Nature Communications, Journal Name: Nature Communications Journal Issue: 1 Vol. 14; ISSN 2041-1723
• Publisher: Nature Publishing GroupCopyright Statement
• Country of Publication: United Kingdom
• Language: English