Flag fault-tolerant error correction, measurement, and quantum computation for cyclic Calderbank-Shor-Steane codes

Theerapat Tansuwannont, Christopher Chamberland, and Debbie Leung
Phys. Rev. A 101, 012342 – Published 24 January 2020

Abstract

Flag qubits have recently been proposed in syndrome extraction circuits to detect high-weight errors arising from fewer faults. The use of flag qubits allows the construction of fault-tolerant protocols with the fewest number of ancillas known to date. In this work, we prove some critical properties of Calderbank-Shor-Steane (CSS) codes constructed from classical cyclic codes that enable the construction of a flag fault-tolerant error correction scheme. We then develop fault-tolerant protocols as well as a family of circuits for flag fault-tolerant error correction and operator measurement, requiring only four ancilla qubits and applicable to cyclic CSS codes of distance 3. The measurement protocol can be further used for logical Clifford gate implementation via quantum gate teleportation. We also provide examples of cyclic CSS codes with large encoding rates.

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  • Received 26 July 2019

DOI:https://doi.org/10.1103/PhysRevA.101.012342

©2020 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Theerapat Tansuwannont1,*, Christopher Chamberland2,1,†, and Debbie Leung3,4,‡

  • 1Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
  • 2IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA
  • 3Institute for Quantum Computing and Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
  • 4Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5

  • *ttansuwannont@uwaterloo.ca
  • christopher.chamberland@ibm.com
  • wcleung@uwaterloo.ca

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Vol. 101, Iss. 1 — January 2020

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