Simulation of quantum circuits by low-rank stabilizer decompositions

@article{Bravyi2019SimulationOQ,
  title={Simulation of quantum circuits by low-rank stabilizer decompositions},
  author={Sergey Bravyi and Dan E. Browne and Padraic Calpin and Earl T. Campbell and David Gosset and Mark Howard},
  journal={Quantum},
  year={2019}
}
Recent work has explored using the stabilizer formalism to classically simulate quantum circuits containing a few non-Clifford gates. The computational cost of such methods is directly related to the notion of stabilizerrank, which for a pure state ψ is defined to be the smallest integer χ such that ψ is a superposition of χ stabilizer states. Here we develop a comprehensive mathematical theory of the stabilizer rank and the related approximate stabilizer rank. We also present a suite of… 

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