# Deep learning Local Reduced Density Matrices for Many-body Hamiltonian Estimation

arXiv: https://arxiv.org/abs/2012.03019 · HTML: https://mlsanity.com/paper/2012.03019/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2020.

## Built on by (most cited first, 1 of 1)

- [Quantum compiling with a variational instruction set for accurate and fast quantum computing](https://mlsanity.com/paper/2203.15574/) (2022)

## Abstract (arXiv)

Human experts cannot efficiently access the physical information of quantum many-body states by simply "reading" the 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 learn from the coefficients of local reduced density matrices to estimate the physical parameters of the many-body 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. By assuming certain constraints on the training set for the sake of balance, 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 estimate the parameters of the states beyond such training regions. For instance, our results show that QubismNet can estimate the magnetic fields near the critical point by learning from the states away from the critical vicinity. Our work illuminates a data-driven way to infer the Hamiltonians that give the designed ground states, and therefore would benefit the existing and future generalizations of quantum technologies such as Hamiltonian-based quantum simulations and state tomography.