The ABCs of color codes


Kubica, A. (2016). The ABCs of color codes. Perimeter Institute. https://pirsa.org/16120028


Kubica, Aleksander. The ABCs of color codes. Perimeter Institute, Dec. 12, 2016, https://pirsa.org/16120028


          @misc{ pirsa_PIRSA:16120028,
            doi = {10.48660/16120028},
            url = {https://pirsa.org/16120028},
            author = {Kubica, Aleksander},
            keywords = {Other},
            language = {en},
            title = {The ABCs of color codes},
            publisher = {Perimeter Institute},
            year = {2016},
            month = {dec},
            note = {PIRSA:16120028 see, \url{https://pirsa.org}}

Aleksander Kubica California Institute of Technology (Caltech)


To build a fully functioning quantum computer, it is necessary to encode quantum information to protect it from noise. Topological codes, such as the color code, naturally protect against local errors and represent our best hope for storing quantum information. Moreover, a quantum computer must also be capable of processing this information. Since the color code has many computationally valuable transversal logical gates, it is a promising candidate for a future quantum computer architecture.

In the talk, I will provide an overview of the color code. First, I will establish a connection between the color code and a well-studied model - the toric code. Then, I will explain how one can implement a universal gate set with the subsystem and the stabilizer color codes in three dimensions using techniques of code switching and gauge fixing. Next, I will discuss the problem of decoding the color code. Finally, I will explain how one can find the optimal error correction threshold by analyzing phase transitions in certain statistical-mechanical models.

The talk is based on http://arxiv.org/abs/1410.0069http://arxiv.org/abs/1503.02065 and recent works with M. Beverland, F. Brandao, N. Delfosse, J. Preskill and K. Svore.