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Parameterized quantum evolution is the main ingredient in variational quantumalgorithms for near-term quantum devices. In digital quantum computing, it hasbeen shown that random parameterized quantum circuits are able to expresscomplex distributions intractable by a classical computer, leading to thedemonstration of quantum supremacy. However, their chaotic nature makesparameter optimization challenging in variational approaches. Evidence ofsimilar classically-intractable expressibility has been recently demonstratedin analog quantum computing with driven many-body systems. A thoroughinvestigation of trainability of such analog systems is yet to be performed. Inthis work, we investigate how the interplay between external driving anddisorder in the system dictates the trainability and expressibility ofinteracting quantum systems. We show that if the system thermalizes, thetraining fails at the expense of the a large expressibility, while the oppositehappens when the system enters the many-body localized (MBL) phase. From thisobservation, we devise a protocol using quenched MBL dynamics which allowsaccurate trainability while keeping the overall dynamics in the quantumsupremacy regime. Our work shows the fundamental connection between quantummany-body physics and its application in machine learning. We conclude our workwith an example application in generative modeling employing a well studiedanalog many-body model of a driven Ising spin chain. Our approach can beimplemented with a variety of available quantum platforms including cold ions,atoms and superconducting circuits

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