Seeding neural network quantum states with tensor network states
This provides a more efficient initialization approach for quantum many-body simulations, though it appears incremental as it builds on existing tensor network and neural network techniques.
The researchers tackled the problem of initializing neural network quantum states for ground-state calculations by developing an efficient method to convert matrix product states into restricted Boltzmann machine wave functions using canonical polyadic decomposition. They demonstrated the method on the transverse-field Ising model, showing it systematically reduces the distance to ground states as decomposition rank increases.
We find an efficient approach to approximately convert matrix product states (MPSs) into restricted Boltzmann machine wave functions consisting of a multinomial hidden unit through a canonical polyadic (CP) decomposition of the MPSs. This method allows us to generate well-behaved initial neural network quantum states for quantum many-body ground-state calculations in polynomial time of the number of variational parameters and systematically shorten the distance between the initial states and the ground states while increasing the rank of the CP decomposition. We demonstrate the efficiency of our method by taking the transverse-field Ising model as an example and discuss possible applications of our method to more general quantum many-body systems in which the ground-state wave functions possess complex nodal structures.