Quantum Entanglement in Deep Learning Architectures

TL;DR

This paper demonstrates that modern deep learning architectures like convolutional and recurrent networks can efficiently represent highly entangled quantum systems, surpassing traditional models in entanglement capacity and efficiency.

Contribution

It establishes a connection between deep learning architectures and tensor networks, showing their ability to support volume-law entanglement scaling and motivating new wave function representations.

Findings

Deep architectures can represent volume-law entanglement efficiently.

Tensor network equivalents reveal information reuse as a key trait.

Supports polynomially more entanglement than RBMs.

Abstract

Modern deep learning has enabled unprecedented achievements in various domains. Nonetheless, employment of machine learning for wave function representations is focused on more traditional architectures such as restricted Boltzmann machines (RBMs) and fully-connected neural networks. In this letter, we establish that contemporary deep learning architectures, in the form of deep convolutional and recurrent networks, can efficiently represent highly entangled quantum systems. By constructing Tensor Network equivalents of these architectures, we identify an inherent reuse of information in the network operation as a key trait which distinguishes them from standard Tensor Network based representations, and which enhances their entanglement capacity. Our results show that such architectures can support volume-law entanglement scaling, polynomially more efficiently than presently employed RBMs. Thus, beyond a quantification of the entanglement capacity of leading deep learning architectures, our analysis formally motivates a shift of trending neural-network based wave function representations closer to the state-of-the-art in machine learning.