Comparison of a quantum error-correction threshold for exact and approximate errors

Mauricio Gutiérrez and Kenneth R. Brown
Phys. Rev. A 91, 022335 – Published 27 February 2015

Abstract

Classical simulations of noisy stabilizer circuits are often used to estimate the threshold of a quantum error-correcting code. Physical noise sources are efficiently approximated by random insertions of Pauli operators. For a single qubit, more accurate approximations that still allow for efficient simulation can be obtained by including Clifford operators and Pauli operators conditional on measurement. We examine the feasibility of employing these expanded error approximations to obtain better threshold estimates. We calculate the level-1 pseudothreshold for the Steane [[7,1,3]] code for amplitude damping and dephasing along a non-Clifford axis. The expanded channels estimate the actual channel action more accurately than the Pauli channels before error correction. However, after error correction, the Pauli twirling approximation yields very accurate estimates of the performance of quantum error-correcting protocols in the presence of the actual noise channel.

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  • Received 4 January 2015

DOI:https://doi.org/10.1103/PhysRevA.91.022335

©2015 American Physical Society

Authors & Affiliations

Mauricio Gutiérrez and Kenneth R. Brown*

  • Schools of Chemistry and Biochemistry; Computational Science and Engineering; and Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, USA

  • *ken.brown@chemistry.gatech.edu

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Issue

Vol. 91, Iss. 2 — February 2015

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