Deep learning quantum states for Hamiltonian predictions

Shi-Ju Ran
Capital Normal University

Human experts cannot efficiently access the physical information of a quantum many-body states by simply "reading" its coefficients, but have to reply on the previous knowledge such as order parameters and quantum measurements. In this work, we demonstrate that convolutional neural network (CNN) can directly learn from the coefficients of many-body states or reduced density matrices to predict the physical parameters of the interacting Hamiltonians, such as coupling strengths and magnetic fields, provided the states as the ground states. We propose QubismNet that consists of two main parts: the Qubism map that visualizes the ground states (or the purified reduced density matrices) as images, and a CNN that maps the images to the target physical parameters. QubismNet exhibits impressive powers of learning and generalization on several quantum spin models. While the training samples are restricted to the states from certain ranges of the parameters, QubismNet can accurately predict the parameters of the states beyond such training regions. For instance, our results show that QubismNet can predict the magnetic fields near the critical point by learning from the states away from the critical vicinity. Our work provides a data-driven way to infer the Hamiltonians that give the designed ground states, and therefore would benefit the existing and future generations of quantum technologies such as Hamiltonian-based quantum simulations and state tomography.

Presentation (PDF File)

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