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Machine learning and signed particles, an alternative and efficient way to simulate quantum systems
Author(s) -
Sellier Jean Michel,
Kapanova Kristina G.,
Leygonie Jacob,
Caron Gaetan Marceau
Publication year - 2019
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.26017
Subject(s) - speedup , computer science , kernel (algebra) , computation , context (archaeology) , quantum , discretization , reduction (mathematics) , reservoir computing , computational complexity theory , algorithm , artificial neural network , theoretical computer science , parallel computing , artificial intelligence , mathematics , physics , quantum mechanics , recurrent neural network , discrete mathematics , mathematical analysis , paleontology , geometry , biology
Recently neural networks have been applied in the context of the signed particle formulation of quantum mechanics to rapidly and reliably compute the Wigner kernel of any provided potential. Important advantages were introduced, such as the reduction of the amount of memory required for the simulation of a quantum system by avoiding the storage of the kernel in a multi‐dimensional array, as well as attainment of consistent speedup by the ability to realize the computation only on the cells occupied by signed particles. An inherent limitation was the number of hidden neurons to be equal to the number of cells of the discretized real space. In this work, anew network architecture is presented, decreasing the number of neurons in its hidden layer, thereby reducing the complexity of the network and achieving an additional speedup. The approach is validated on a onedimensional quantum system consisting of a Gaussian wave packet interacting with a potential barrier.