Quantum Information Processing

, Volume 15, Issue 8, pp 3065–3079

Analytical error analysis of Clifford gates by the fault-path tracer method

  • Smitha Janardan
  • Yu Tomita
  • Mauricio Gutiérrez
  • Kenneth R. Brown
Article

DOI: 10.1007/s11128-016-1330-z

Cite this article as:
Janardan, S., Tomita, Y., Gutiérrez, M. et al. Quantum Inf Process (2016) 15: 3065. doi:10.1007/s11128-016-1330-z
Part of the following topical collections:
  1. Quantum Computer Science

Abstract

We estimate the success probability of quantum protocols composed of Clifford operations in the presence of Pauli errors. Our method is derived from the fault-point formalism previously used to determine the success rate of low-distance error correction codes. Here we apply it to a wider range of quantum protocols and identify circuit structures that allow for efficient calculation of the exact success probability and even the final distribution of output states. As examples, we apply our method to the Bernstein–Vazirani algorithm and the Steane [[7,1,3]] quantum error correction code and compare the results to Monte Carlo simulations.

Keywords

Quantum error correction Thresholds Bernstein–Vazirani algorithm Clifford circuits 

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Smitha Janardan
    • 1
  • Yu Tomita
    • 1
  • Mauricio Gutiérrez
    • 1
  • Kenneth R. Brown
    • 1
  1. 1.Schools of Chemistry and Biochemistry, Computational Science and Engineering, and PhysicsGeorgia Institute of TechnologyAtlantaUSA