Protected gates for topological quantum field theories

  title={Protected gates for topological quantum field theories},
  author={Michael Beverland and Oliver Buerschaper and Robert Koenig and Fernando Pastawski and John Preskill and Sumit Sijher},
  journal={arXiv: Quantum Physics},
We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators --- for example, a constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically-local bounded-strength Hamiltonian. Locality-preserving logical gates of topological codes are intrinsically fault tolerant because spatially… 
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