Classifying topological neural network quantum states via diffusion maps

• URL: http://arxiv.org/abs/2301.02683v1
• Date: Fri, 6 Jan 2023 19:00:21 GMT
• Title: Classifying topological neural network quantum states via diffusion maps
• Authors: Yanting Teng, Subir Sachdev, Mathias S. Scheurer
• Abstract summary: We discuss and demonstrate an unsupervised machine-learning procedure to detect topological order in quantum many-body systems. We use a restricted Boltzmann machine to define a variational ansatz for the low-energy spectrum. We show that for the diffusion map, the required similarity measure of quantum states can be defined in terms of the network parameters.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We discuss and demonstrate an unsupervised machine-learning procedure to detect topological order in quantum many-body systems. Using a restricted Boltzmann machine to define a variational ansatz for the low-energy spectrum, we sample wave functions with probability decaying exponentially with their variational energy; this defines our training dataset that we use as input to a diffusion map scheme. The diffusion map provides a low-dimensional embedding of the wave functions, revealing the presence or absence of superselection sectors and, thus, topological order. We show that for the diffusion map, the required similarity measure of quantum states can be defined in terms of the network parameters, allowing for an efficient evaluation within polynomial time. However, possible ''gauge redundancies'' have to be carefully taken into account. As an explicit example, we apply the method to the toric code.

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