Learning Energy-Based Representations of Quantum Many-Body States
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 physi...
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Zusammenfassung: | 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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DOI: | 10.48550/arxiv.2304.04058 |