Error correction with the color code

          @misc{ pirsa_PIRSA:19110136,
            doi = {10.48660/19110136},
            url = {https://pirsa.org/19110136},
            author = {Kubica, Aleksander},
            keywords = {Quantum Information},
            language = {en},
            title = {Error correction with the color code},
            publisher = {Perimeter Institute},
            year = {2019},
            month = {nov},
            note = {PIRSA:19110136 see, \url{https://pirsa.org}}
          }
          

Abstract

The color code is a topological quantum code with many valuable fault-tolerant logical gates. Its two-dimensional version may soon be realized with currently available superconducting hardware despite constrained qubit connectivity. In the talk, I will focus on how to perform error correction with the color code in d ≥ 2 dimensions. I will describe an efficient color code decoder, the Restriction Decoder, which uses as a subroutine any toric code decoder. I will also present numerical estimates of the storage threshold of the Restriction Decoder for the triangular color code against circuit-level depolarizing noise. Based on arXiv:1905.07393 and arXiv:1911.00355.