PIRSA:13090069 Scientific Series Quantum Foundations

DOI10.48660/13090069

Series: Perimeter Institute Quantum Discussions

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}}
}

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.

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