Quantum dynamics in transverse-field Ising models from classical networks

摘要

The efficient representation of quantum many-body states with classicalresources is a key challenge in quantum many-body theory. In this work weanalytically construct classical networks for the description of the quantumdynamics in transverse-field Ising models that can be solved efficiently usingMonte Carlo techniques. Our perturbative construction encodes time-evolvedquantum states of spin-1/2 systems in a network of classical spins with localcouplings and can be directly generalized to other spin systems and higherspins. Using this construction we compute the transient dynamics in one, two,and three dimensions including local observables, entanglement production, andLoschmidt amplitudes using Monte Carlo algorithms and demonstrate the accuracyof this approach by comparisons to exact results. We include a mapping toequivalent artificial neural networks, which were recently introduced toprovide a universal structure for classical network wave functions.