Abstract
Topological subsystem color codes add an important feature to the advantages of topological codes: error tracking only involves measuring two local operators in a two-dimensional setting. Unfortunately, currently known methods for computing with them are highly unpractical. We give a mechanism for implementing 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.
Highlights
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
An error correcting code [6, 7] protects quantum information from decoherence by means of redundancy. This is achieved by selecting a set of commuting observables, called check operators, that are initialized with a specific set of values, defining a code subspace
The failure probability decreases exponentially with the system size [8]. This behavior is reminiscent of a phase transition, and error correction can be rephrased in terms of a statistical mechanical model [4, 8, 9]
Summary
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. As BaconShor codes, TSCCs only require 2-local measurements in a 2D setting but, unlike them, they posses a threshold in the large lattice limit and allow the use of error correction techniques that are specific of topological codes. This technique plays with the possibility of changing the geometry of the code over time and allows to implement gates and to initialize and measure encoded qubits in a protected way.
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