Chin. Phys. Lett.  2021, Vol. 38 Issue (11): 110301    DOI: 10.1088/0256-307X/38/11/110301
Deep Learning Quantum States for Hamiltonian Estimation
Xinran Ma1, Z. C. Tu1, and Shi-Ju Ran2*
1Department of Physics, Beijing Normal University, Beijing 100875, China
2Department of Physics, Capital Normal University, Beijing 100048, China
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Xinran Ma, Z. C. Tu, and Shi-Ju Ran 2021 Chin. Phys. Lett. 38 110301
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Abstract Human experts cannot efficiently access 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. We demonstrate that convolutional neural network (CNN) can learn from coefficients of many-body states or reduced density matrices to estimate 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. 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 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.
Received: 15 August 2021      Express Letter Published: 11 October 2021
PACS:  03.67.Ac (Quantum algorithms, protocols, and simulations)  
  02.30.Zz (Inverse problems)  
  03.65.Wj (State reconstruction, quantum tomography)  
  03.67.Lx (Quantum computation architectures and implementations)  
  07.05.Mh (Neural networks, fuzzy logic, artificial intelligence)  
  75.10.Jm (Quantized spin models, including quantum spin frustration)  
Fund: Supported by the National Natural Science Foundation of China (Grant Nos. 12004266, 11834014 and 11975050), the Beijing Natural Science Foundation (Grant Nos. 1192005 and Z180013), the Foundation of Beijing Education Committees (Grant No. KM202010028013), and the Academy for Multidisciplinary Studies, Capital Normal University.
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Xinran Ma
Z. C. Tu
and Shi-Ju Ran
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