Dynamical simulation via quantum machine learning with provable generalization

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Dynamical simulation and QML are both promising fields, and our work is the first to explore their intersection. We show that QML generalization bounds can guarantee good performance of certain dynamical simulation algorithms with minimal training data required. In the process, we develop a new simulation algorithm that is promising.

We unify dynamical simulation and quantum machine learning (QML) under one umbrella. We use QML generalization bounds to rigously bound the errors of a new dynamical simulation algorithm that we propose. With our new algorithm, we simulate 20 times longer than Trotterization on IBM’s quantum hardware.

Our main result is a rigorous lower bound on the simulation fidelity as a function of the amount of training data, for product state training. We also implement our algorithm on IBM’s quantum hardware with good performance.

For details see

“Dynamical simulation via quantum machine learning with provable generalization”, Joe Gibbs, Zoë Holmes, Matthias C. Caro, Nicholas Ezzell, Hsin-Yuan Huang, Lukasz Cincio, Andrew T. Sornborger, Patrick J. Coles. arXiv:2204.10269.