Learning quantum properties from short-range correlations using multi-task networks
Nature Communications volume 15, Article number: 8796 (2024 ) Cite this article
Characterizing multipartite quantum systems is crucial for quantum computing and many-body physics. The problem, however, becomes challenging when the system size is large and the properties of interest involve correlations among a large number of particles. Here we introduce a neural network model that can predict various quantum properties of many-body quantum states with constant correlation length, using only measurement data from a small number of neighboring sites. The model is based on the technique of multi-task learning, which we show to offer several advantages over traditional single-task approaches. Through numerical experiments, we show that multi-task learning can be applied to sufficiently regular states to predict global properties, like string order parameters, from the observation of short-range correlations, and to distinguish between quantum phases that cannot be distinguished by single-task networks. Remarkably, our model appears to be able to transfer information learnt from lower dimensional quantum systems to higher dimensional ones, and to make accurate predictions for Hamiltonians that were not seen in the training.
The experimental characterization of many-body quantum states is an essential task in quantum information and computation. Neural networks provide a powerful approach to quantum state characterization1,2,3,4, enabling a compact representation of sufficiently structured quantum states5. In recent years, different types of neural networks have been successfully utilized to predict properties of quantum systems, including quantum fidelity6,7,8 and other measures of similarity9,10, quantum entanglement11,12,13, entanglement entropy1,14,15, two-point correlations1,2,14 and Pauli expectation values4,16, as well as to identify phases of matter17,18,19,20,21.
