Universal transversal gates with color codes - a simplified approach
Kubica, Aleksander · Beverland, Michael E.
Original · EN
We provide a simplified, yet rigorous presentation of the ideas from Bombín's paper "Gauge Color Codes" [arXiv:1311.0879v3]. Our presentation is self-contained, and assumes only basic concepts from quantum error correction. We provide an explicit construction of a family of color codes in arbitrary dimensions and describe some of their crucial properties. Within this framework, we explicitly show how to transversally implement the generalized phase gate Rₙ=diag(1,e²πⁱ/²ⁿ), which deviates from the method in "Gauge Color Codes", allowing an arguably simpler proof. We describe how to implement the Hadamard gate H fault-tolerantly using code switching. In three dimensions, this yields, together with the transversal CNOT, a fault-tolerant universal gate set {H,CNOT,R₃} without state-distillation.
English translation
This paper has no Arabic translation yet. Be the first: it takes a few seconds, and the result is stored for every future reader.