Rectangular surface code under biased noise

Jonghyun Lee, Jooyoun Park, Jun Heo

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


To date, the surface code has become a promising candidate for quantum error correcting codes because it achieves a high threshold and is composed of only the nearest gate operations and low-weight stabilizers. Here, we have exhibited that the logical failure rate can be enhanced by manipulating the lattice size of surface codes that they can show an enormous improvement in the number of physical qubits for a noise model where dephasing errors dominate over relaxation errors. We estimated the logical error rate in terms of the lattice size and physical error rate. When the physical error rate was high, the parameter estimation method was applied, and when it was low, the most frequently occurring logical error cases were considered. By using the minimum weight perfect matching decoding algorithm, we obtained the optimal lattice size by minimizing the number of qubits to achieve the required failure rates when physical error rates and bias are provided.

Original languageEnglish
Article number231
JournalQuantum Information Processing
Issue number7
Publication statusPublished - 2021 Jul

Bibliographical note

Funding Information:
This research was supported by the MSIT (Ministry of Science and ICT), Korea, under the ITRC (Information Technology Research Center) support program (IITP-2021-2018-0-01402) supervised by the IITP (Institute for Information and Communications Technology Planning and Evaluation). This work was supported as part of Military Crypto Research Center funded by Defense Acquisition Program Administration (DAPA) and Agency for Defense Development (ADD).

Publisher Copyright:
© 2021, The Author(s).


  • Biased noise channel
  • Quantum error correcting code
  • Rectangular surface code

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Statistical and Nonlinear Physics
  • Theoretical Computer Science
  • Signal Processing
  • Modelling and Simulation
  • Electrical and Electronic Engineering


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