Science Advances

Supplementary Materials

This PDF file includes:

  • Section S1. A brief introduction to generative models
  • Section S2. Representational power and generalization ability
  • Section S3. Reduction of typical generative models to factor graphs
  • Section S4. Universal approximation theorem
  • Section S5. Proof of theorem 2
  • Section S6. NP hardness for preparation of an arbitrary QGM state |Q
  • Section S7. Parent Hamiltonian of the state |Q
  • Section S8. Training and inference in the QGM
  • Section S9. Proof of theorem 3
  • Section S10. Applying the QGM to practical examples
  • Fig. S1. Parameter space of factor graph and QGM.
  • Fig. S2. Probabilistic graphical models.
  • Fig. S3. Energy-based neural networks.
  • Fig. S4. Simulating graphs of unbounded degrees with graphs of constantly bounded degrees.
  • Fig. S5. Illustration of the universal approximation theorem by a restricted Boltzmann machine.
  • Fig. S6. #P-hardness for the QGM.
  • Fig. S7. Contraction between two local tensors using the structure of QGM state and conditioned variables.
  • Fig. S8. Construction of the history state.
  • Fig. S9. Flow chart for a machine learning process using the QGM.
  • References (3840)

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