PIRSA:13090069

Universal fault-tolerant quantum computation with only transversal gates and error correction

Paetznick, A. (2013). Universal fault-tolerant quantum computation with only transversal gates and error correction. Perimeter Institute. https://pirsa.org/13090069

Paetznick, Adam. Universal fault-tolerant quantum computation with only transversal gates and error correction. Perimeter Institute, Sep. 25, 2013, https://pirsa.org/13090069 

          @misc{ pirsa_PIRSA:13090069,
            doi = {10.48660/13090069},
            url = {https://pirsa.org/13090069},
            author = {Paetznick, Adam},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Universal fault-tolerant quantum computation with only transversal gates and error correction},
            publisher = {Perimeter Institute},
            year = {2013},
            month = {sep},
            note = {PIRSA:13090069 see, \url{https://pirsa.org}}
          }

Adam Paetznick

Talk numberPIRSA:13090069
DOI10.48660/13090069
Collection
Talk Type Scientific Series
Subject

Abstract

Transversal implementations of encoded unitary gates are highly desirable for fault-tolerant quantum computation.  It is known, however, that transversal gates alone cannot be computationally universal.  I will show that the limitation on universality can be circumvented using only fault-tolerant error correction, which is already required anyway.  This result applies to ``triorthogonal'' stabilizer codes, which were recently introduced by Bravyi and Haah for state distillation.  I will show that triothogonal codes admit transversal implementation of the controlled-controlled-Z gate, and then demonstrate a transversal Hadamard construction which uses error correction to preserve the codespace. I will also discuss how to adapt the distillation procedure of Bravyi and Haah to Toffoli gates, improving on existing Toffoli distillation schemes.