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

Craig Gidney

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arXiv · 1910.00363

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

Craig Gidney

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Abstract

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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Craig Gidney. 2019-09-30. Surface code dislocations have code distance L+O(1). https://arxiv.org/abs/1910.00363

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