860 research outputs found
Topological Subsystem Codes
We introduce a family of 2D topological subsystem quantum error-correcting
codes. The gauge group is generated by 2-local Pauli operators, so that 2-local
measurements are enough to recover the error syndrome. We study the
computational power of code deformation in these codes, and show that
boundaries cannot be introduced in the usual way. In addition, we give a
general mapping connecting suitable classical statistical mechanical models to
optimal error correction in subsystem stabilizer codes that suffer from
depolarizing noise.Comment: 16 pages, 11 figures, explanations added, typos correcte
Clifford Gates by Code Deformation
Topological subsystem color codes add to the advantages of topological codes
an important feature: error tracking only involves measuring 2-local operators
in a two dimensional setting. Unfortunately, known methods to compute with them
were highly unpractical. We give a mechanism to implement all Clifford gates by
code deformation in a planar setting. In particular, we use twist braiding and
express its effects in terms of certain colored Majorana operators.Comment: Extended version with more detail
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