Quantum error-correcting codes from Abelian anyon theories


Ellison, T. (2023). Quantum error-correcting codes from Abelian anyon theories. Perimeter Institute. https://pirsa.org/23120028


Ellison, Tyler. Quantum error-correcting codes from Abelian anyon theories. Perimeter Institute, Dec. 06, 2023, https://pirsa.org/23120028


          @misc{ pirsa_PIRSA:23120028,
            doi = {10.48660/23120028},
            url = {https://pirsa.org/23120028},
            author = {Ellison, Tyler},
            keywords = {Condensed Matter},
            language = {en},
            title = {Quantum error-correcting codes from Abelian anyon theories},
            publisher = {Perimeter Institute},
            year = {2023},
            month = {dec},
            note = {PIRSA:23120028 see, \url{https://pirsa.org}}

Tyler Ellison Yale University

Talk Type Scientific Series


To perform reliable quantum computations in the midst of noise from the environment, it is imperative to use a quantum error-correcting code — i.e., a scheme for redundantly encoding information so that errors may be detected and corrected as they occur. One of the most promising classes of quantum error-correcting codes are those based on topological phases of matter, such as the celebrated toric code. Although there is a rich classification of topological phases of matter, the toric code has by far received the most attention as a practical quantum error-correcting code, due to its simple representation within the stabilizer formalism.

In this talk, I will discuss three works in which we extend the stabilizer formalism to topological orders beyond that of the toric code. This includes the construction of two-dimensional stabilizer codes characterized by Abelian topological orders with gapped boundaries, three-dimensional stabilizer codes that host arbitrary two-dimensional Abelian topological orders on their surface, and two-dimensional subsystem codes also characterized by arbitrary Abelian topological orders. This work thus opens the door to encoding and processing quantum information using the exotic properties exhibited by the wide range of Abelian topological phases of matter.


Zoom link https://pitp.zoom.us/j/94640905425?pwd=aDd0Qnl1TUU0QytaNWJJLzEyZlQrQT09