Efficient classical simulation of random shallow 2D quantum circuits

@article{Napp2020EfficientCS,
  title={Efficient classical simulation of random shallow 2D quantum circuits},
  author={John Napp and Rolando L. La Placa and Alexander M. Dalzell and Fernando G. S. L. Brand{\~a}o and Aram Wettroth Harrow},
  journal={ArXiv},
  year={2020},
  volume={abs/2001.00021}
}
Random quantum circuits are commonly viewed as hard to simulate classically. In some regimes this has been formally conjectured, and there had been no evidence against the more general possibility that for circuits with uniformly random gates, approximate simulation of typical instances is almost as hard as exact simulation. We prove that this is not the case by exhibiting a shallow circuit family with uniformly random gates that cannot be efficiently classically simulated near-exactly under… 

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