Emergence of global receptive fields capturing multipartite quantum correlations

TL;DR

This paper demonstrates how neural network weight analysis reveals global structures in quantum states, enabling the creation of exact classical models for complex multipartite entanglement.

Contribution

It introduces a novel approach to interpret neural quantum states by monitoring weight space, leading to exact classical representations of Dicke states.

Findings

Identification of global convolutional structures in RBMs during quantum state learning

Development of an exact two-parameter classical model for Dicke states

Insights into neural network design for non-local quantum data

Abstract

In quantum physics, even simple data with a well-defined structure at the wave function level can be characterized by extremely complex correlations between its constituent elements. The inherent non-locality of the quantum correlations generally prevents one from providing their simple and transparent interpretation, which also remains a challenging problem for advanced classical techniques that approximate quantum states with neural networks. Here we show that monitoring the neural network weight space while learning quantum statistics from measurements allows to develop physical intuition about complex multipartite patterns and thus helps to construct more effective classical representations of the wave functions. Particularly, we observe the formation of distinct global convolutional structures, receptive fields in the hidden layer of the Restricted Boltzmann Machine (RBM) within the neural quantum tomography of the highly-entangled Dicke states. On this basis we propose an exact two-parameter classical representation not only for a specific quantum wave function, but for the whole family of the N-qubit Dicke states of different entanglement. Our findings suggest a fresh look at constructing convolutional neural networks for processing data with non-local patterns and pave the way for developing exact learning-based representations of entangled quantum states.