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Conference proceedings/Conference proceedings - IEEE International Conference on Systems, Man, and Cybernetics

Learning Quantum Distributions Based on Normalizing Flow

Li Li, Yong Wang, Shuming Cheng, Lijun Liu

Published Oct 1, 2023• 0 citations
Publisher

Abstract

Learning many-body quantum systems is of fundamental importance in quantum information processing, however, it is a challenging task which typically requires estimating quantum distributions of dimensionality exponentially scaling to the system size. As generative models have shown a great scalability to learn high-dimensional distributions and found wide applications in the domain of image and text, they can be a powerful tool to facilitate us to accomplish the challenging quantum tasks. In this work, we propose using normalizing flow (NF) models with fast sampling to learn discrete quantum distributions for quantum state tomography. Particularly, three NF models, including denoising flow, argmax flow, and tree flow, are first adapted to the task of explicit quantum probability density estimation. We then perform extensive experiments on a large scale of quantum systems, and our numerical results demonstrate that these discrete NFs admit an excellent sampling efficiency in the sense that they are insensitive to the system size to learn the high-dimensional quantum distributions, without compromising the learning performance. Finally, in comparison to the other generative models, such as autoregressive, the NFs avoid the problem of slow sequential sampling.

DOI
10.1109/smc53992.2023.10394048

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Abstract The exact description of many-body quantum systems represents one of the major challenges in modern physics, because it requires an amount of computational resources that scales exponentially with the size of the system. Simulating the evolution of a state, or even storing its description, rapidly becomes intractable for exact classical algorithms. Recently, machine learning techniques, in the form of restricted Boltzmann machines, have been proposed as a way to efficiently represent certain quantum states with applications in state tomography and ground state estimation. Here, we introduce a practically usable deep architecture for representing and sampling from probability distributions of quantum states. Our representation is based on variational auto-encoders, a type of generative model in the form of a neural network. We show that this model is able to learn efficient representations of states that are easy to simulate classically and can compress states that are not classically tractable. Specifically, we consider the learnability of a class of quantum states introduced by Fefferman and Umans. Such states are provably hard to sample for classical computers, but not for quantum ones, under plausible computational complexity assumptions. The good level of compression achieved for hard states suggests these methods can be suitable for characterizing states of the size expected in first generation quantum hardware.