Expressibility and trainability of parametrized analog quantum systems for machine learning applications

Parametrized quantum evolution is the main ingredient in variational quantum algorithms for near-term quantum devices. In digital quantum computing, it has been shown that random parametrized quantum circuits are able to express complex distributions intractable by a classical computer, leading to the demonstration of quantum supremacy. However, their chaotic nature makes parameter optimization challenging in variational approaches. Evidence of similar classically intractable expressibility has been recently demonstrated in analog quantum computing with driven many-body systems. A thorough investigation of trainability of such analog systems is yet to be performed. In this work we investigate how the interplay between external driving and disorder in the system dictates the trainability and expressibility of interacting quantum systems. We show that if the system thermalizes, the training fails at the expense of the large expressibility, while the opposite happens when the system enters the many-body localized (MBL) phase. From this observation we devise a protocol using quenched MBL dynamics which allows accurate trainability while keeping the overall dynamics in the quantum supremacy regime. Our work shows the fundamental connection between quantum many-body physics and its application in machine learning. We conclude our work with an example application in generative modeling employing a well studied analog many-body model of a driven Ising spin chain. Our approach can be implemented with a variety of available quantum platforms including cold ions, atoms, and superconducting circuits.