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Équipe de Recherche en Physique de l'Information Quantique



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@Article{FV12a,
Year = {2012},
Abstract = {Tensor network states are powerful variational ans¨atze for many-body ground states of quantum lattice models.
The use of Monte Carlo sampling techniques in tensor network approaches significantly reduces the cost
of tensor contractions, potentially leading to a substantial increase in computational efficiency. Previous proposals
are based on a Markov chain Monte Carlo scheme generated by locally updating configurations and, as
such, must deal with equilibration and autocorrelation times, which result in a reduction of efficiency. Here we
propose a perfect sampling scheme, with vanishing equilibration and autocorrelation times, for unitary tensor
networks – namely tensor networks based on efficiently contractible, unitary quantum circuits, such as unitary
versions of the matrix product state (MPS) and tree tensor network (TTN), and the multi-scale entanglement
renormalization ansatz (MERA). Configurations are directly sampled according to their probabilities in the
wavefunction, without resorting to a Markov chain process. We also describe a partial sampling scheme that
can result in a dramatic (basis-dependent) reduction of sampling error.},
author = {A. Ferris and G. Vidal},
title = {Perfect Sampling with Unitary Tensor Networks},
journal = {Phys. Rev. B},
number = {85},
pages = {165146},
eprint = {arXiv:1201.3974},
local-url = {PhysRevB.85.165146.pdf}}