Low overhead Clifford gates from joint measurements in surface, color, and hyperbolic codes

@article{Lavasani2018LowOC,
  title={Low overhead Clifford gates from joint measurements in surface, color, and hyperbolic codes},
  author={Ali Lavasani and Maissam Barkeshli},
  journal={Physical Review A},
  year={2018}
}
One of the most promising routes towards fault-tolerant quantum computation utilizes topological quantum error correcting codes, such as the $\mathbb{Z}_2$ surface code. Logical qubits can be encoded in a variety of ways in the surface code, based on either boundary defects, holes, or bulk twist defects. However proposed fault-tolerant implementations of the Clifford group in these schemes are limited and often require unnecessary overhead. For example, the Clifford phase gate in certain planar… 
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