Performance of quantum error correction with coherent errors

Eric Huang, Andrew C. Doherty, and Steven Flammia
Phys. Rev. A 99, 022313 – Published 12 February 2019

Abstract

We compare the performance of quantum error correcting codes when memory errors are unitary with the more familiar case of dephasing noise. For a wide range of codes, we analytically compute the effective logical channel that results when the error correction steps are performed noiselessly. Our examples include the entire family of repetition codes, the five-qubit, Steane, Shor, and surface codes. When errors are measured in terms of the diamond norm, we find that the error correction is typically much more effective for unitary errors than for dephasing. We observe this behavior for a wide range of codes after a single level of encoding, and in the thresholds of concatenated codes using hard decoders. We show that this holds with great generality by proving a bound on the performance of any stabilizer code when the noise at the physical level is unitary. By comparing the diamond norm error D of the logical qubit with the same quantity at the physical level D, we show that DcDd where d is the distance of the code and c is a constant that depends on the code but not on the error. This bound compares very favorably to the performance of error correction for dephasing noise and other Pauli channels, where an error correcting code of odd distance d will exhibit a scaling DD(d+1)/2.

  • Figure
  • Figure
  • Figure
  • Received 30 May 2018

DOI:https://doi.org/10.1103/PhysRevA.99.022313

©2019 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Eric Huang1, Andrew C. Doherty1, and Steven Flammia1,2

  • 1Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney, NSW 2006, Australia
  • 2Yale Quantum Institute, Yale University, New Haven, Connecticut 06520, USA

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 99, Iss. 2 — February 2019

Reuse & Permissions
Access Options
CHORUS

Article Available via CHORUS

Download Accepted Manuscript
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review A

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×