A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes

@article{Bravyi2008ANT,
  title={A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes},
  author={Sergey Bravyi and Barbara M. Terhal},
  journal={New Journal of Physics},
  year={2008},
  volume={11},
  pages={043029}
}
We study properties of stabilizer codes that permit a local description on a regular D-dimensional lattice. Specifically, we assume that the stabilizer group of a code (the gauge group for subsystem codes) can be generated by local Pauli operators such that the support of any generator is bounded by a hypercube of size O(1). Our first result concerns the optimal scaling of the distance d with the linear size of the lattice L. We prove an upper bound d=O(LD-1) which is tight for D=1, 2. This… 

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