Classical simulation of quantum computation, the Gottesman-Knill theorem, and slightly beyond

@article{Nes2010ClassicalSO,
  title={Classical simulation of quantum computation, the Gottesman-Knill theorem, and slightly beyond},
  author={Maarten Van Den Nes},
  journal={Quantum Information \& Computation},
  year={2010},
  volume={10},
  pages={258-271}
}
We study classical simulation of quantum computation, taking the Gottesman-Knilltheorem as a starting point. We show how each Clifford circuit can be reduced to anequivalent, manifestly simulatable circuit (normal form). This provides a simple proofof the Gottesman-Knill theorem without resorting to stabilizer techniques. The normalform highlights why Clifford circuits have such limited computational power in spiteof their high entangling power. At the same time, the normal form shows how… 
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