PIRSA:17080041

Bounding and building fault-tolerant quantum circuits on stabilizer codes

Yoder, T. (2017). Bounding and building fault-tolerant quantum circuits on stabilizer codes . Perimeter Institute. https://pirsa.org/17080041

Yoder, Theodore. Bounding and building fault-tolerant quantum circuits on stabilizer codes . Perimeter Institute, Aug. 09, 2017, https://pirsa.org/17080041 

          @misc{ pirsa_PIRSA:17080041,
            doi = {10.48660/17080041},
            url = {https://pirsa.org/17080041},
            author = {Yoder, Theodore},
            keywords = {Other},
            language = {en},
            title = {Bounding and building fault-tolerant quantum circuits on stabilizer codes },
            publisher = {Perimeter Institute},
            year = {2017},
            month = {aug},
            note = {PIRSA:17080041 see, \url{https://pirsa.org}}
          }

Theodore Yoder

Massachusetts Institute of Technology (MIT)

Talk number
PIRSA:17080041
Collection
Talk Type
Subject
Abstract

Transversality is one of the most desirable features of fault-tolerant circuits because it automatically limits the propagation of errors. However, it was shown by Eastin & Knill that no universal set of quantum gates on any quantum code is transversal. In this talk, we strengthen this result for stabilizer codes to say that transversal gates must in fact be contained in the Clifford hierarchy. Moreover, we present new circuits on Bacon-Shor codes that saturate our bounds. In particular, we show how a k-qubit controlled-Z gate can be implemented by a transversal circuit on m-by-m^k Bacon-Shor codes and provide some estimates of its performance in terms of pseudo-thresholds and resource overhead.