Learning Energy-Based Representations of Quantum Many-Body States

• URL: http://arxiv.org/abs/2304.04058v1
• Date: Sat, 8 Apr 2023 16:01:44 GMT
• Title: Learning Energy-Based Representations of Quantum Many-Body States
• Authors: Abhijith Jayakumar, Marc Vuffray, Andrey Y. Lokhov
• Abstract summary: An ideal representation of a quantum state combines a succinct characterization informed by the system's structure and symmetries, along with the ability to predict the physical observables of interest. Here, we propose a new generative energy-based representation of quantum many-body states derived from Gibbs distributions used for modeling the thermal states of classical spin systems. Our results show that such a representation can be efficiently learned from data using exact algorithms in a form that enables the prediction of expectation values of physical observables.
• Score: 14.781921087738969
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Efficient representation of quantum many-body states on classical computers is a problem of enormous practical interest. An ideal representation of a quantum state combines a succinct characterization informed by the system's structure and symmetries, along with the ability to predict the physical observables of interest. A number of machine learning approaches have been recently used to construct such classical representations [1-6] which enable predictions of observables [7] and account for physical symmetries [8]. However, the structure of a quantum state gets typically lost unless a specialized ansatz is employed based on prior knowledge of the system [9-12]. Moreover, most such approaches give no information about what states are easier to learn in comparison to others. Here, we propose a new generative energy-based representation of quantum many-body states derived from Gibbs distributions used for modeling the thermal states of classical spin systems. Based on the prior information on a family of quantum states, the energy function can be specified by a small number of parameters using an explicit low-degree polynomial or a generic parametric family such as neural nets, and can naturally include the known symmetries of the system. Our results show that such a representation can be efficiently learned from data using exact algorithms in a form that enables the prediction of expectation values of physical observables. Importantly, the structure of the learned energy function provides a natural explanation for the hardness of learning for a given class of quantum states.

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