Abstract
Parameterized 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 parameterized 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 a 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
Highlights
The recent achievement of quantum supremacy [1], the ability of quantum systems to compute tasks that are intractable by a classical computer, stands as an important milestone for noisy intermediate-scale quantum (NISQ) devices [2]
We focus on four generic phases depending on whether the dynamics is thermalized or many-body localized (MBL) [35,36] and whether a continuous drive is applied
We find that, evolving under the dynamics resulting from a series of quenches between randomized disorder configurations, the system in all four phases are capable of reaching the quantum supremacy regime, illustrating its high expressibility beyond a classical computer
Summary
The recent achievement of quantum supremacy [1], the ability of quantum systems to compute tasks that are intractable by a classical computer, stands as an important milestone for noisy intermediate-scale quantum (NISQ) devices [2]. In the case when such ansatz is not known or implementable, it is desirable to exploit high expressibility of some NISQ devices to generate an unbiased guess. The latter is known as “hardware efficient” [8]. In this work we analyze the expressibility and trainability of analog quantum devices focusing on parametrized driven quantum many-body systems. We show that these properties are intimately related to phases of the system. The final learning accuracy depends solely on the phase of the system
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