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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

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.