Corpus ID: 203610212

Surface code dislocations have code distance L+O(1)

@article{Gidney2019SurfaceCD,
  title={Surface code dislocations have code distance L+O(1)},
  author={Craig Gidney},
  journal={arXiv: Quantum Physics},
  year={2019}
}
  • C. Gidney
  • Published 30 September 2019
  • Physics
  • arXiv: Quantum Physics
In [Hastings et al 2014] it is stated that the code distance of a logical qubit stored using dislocations is 2L + O(1), where L is the separation between the dislocation twists. This code distance assumed only physical X and Z errors are permitted. This short note shows that, when Y errors are allowed, the code distance reduces to L + O(1). See Figure 1. 

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References

SHOWING 1-3 OF 3 REFERENCES
Reduced space-time and time costs Ising dislocation codes and arbitrary ancillas
TLDR
An amortized analysis is used to show that even in a parallel setting this leads to only a constant factor slowdown as opposed to the logarithmic slowdown that might be expected naively. Expand
Low overhead Clifford gates from joint measurements in surface, color, and hyperbolic codes
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 encodedExpand
Craig Gidney: craiggidney@google.com ar X
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  • 2019