Surface code design for asymmetric error channels

IET Quantum Communication, vol. 3, pp. 174–183

Abstract

Abstract Surface codes are quantum error correcting codes typically defined on a 2D array of qubits. A [ d x , d z ] surface code design is being introduced, where d x ( d z ) represents the distance of the code for bit (phase) error correction, motivated by the fact that the severity of bit flip and phase flip errors in the physical quantum system is asymmetric. We present pseudo‐threshold and threshold values for the proposed surface code design for asymmetric error channels in the presence of various degrees of asymmetry of , errors in a depolarisation channel. We demonstrate that compared to symmetric surface codes, our asymmetric surface codes can provide almost double the pseudo‐threshold rates while requiring less than half the number of physical qubits in the presence of increasing asymmetry in the error channel. Our results show that for low degree of asymmetry, it is advantageous to increase d x along with d z . However, as the asymmetry of the channel increases, higher pseudo‐threshold is obtained with increasing d z when d x is kept constant at a low value. Additionally, we also show that the advantage in the pseudo‐threshold rates begins to saturate for any possible degree of asymmetry in the error channel as the surface code asymmetry is continued to be increased.

Authors 5

1. Utkarsh Azad corresponding

   Xanadu Quantum Technologies (Canada) · International Institute of Information Technology, Hyderabad

   Affiliation as printed

   Center for Computational Natural Sciences and Bioinformatics International Institute of Information Technology Hyderabad India

   Center for Quantum Science and Technology International Institute of Information Technology Hyderabad India

   Xanadu Toronto Ontario Canada

   Center for Computational Natural Sciences and Bioinformatics International Institute of Information Technology Hyderabad India

   Center for Quantum Science and Technology International Institute of Information Technology Hyderabad India

   Xanadu Toronto Ontario Canada

2. Shilpa Mahato

   Indian Institute of Technology Dhanbad

   Affiliation as printed

   Department of Physics Indian Institute of Technology Dhanbad Dhanbad India

   Department of Physics Indian Institute of Technology Dhanbad Dhanbad India

3. Rijul Sachdeva Aachen

   Forschungszentrum Jülich · Jülich Supercomputing Centre · RWTH Aachen University

   Affiliation as printed

   Jülich Supercomputing Center Forschungszentrum Jülich Jülich Germany

   RWTH Aachen University Aachen Germany

   Jülich Supercomputing Center Forschungszentrum Jülich Jülich Germany

4. Debasmita Bhoumik

   Indian Statistical Institute

   Affiliation as printed

   Advanced Computing & Microelectronics Unit Indian Statistical Institute Kolkata India

   Advanced Computing & Microelectronics Unit Indian Statistical Institute Kolkata India

5. Ritajit Majumdar

   Indian Statistical Institute

   Affiliation as printed

   Advanced Computing & Microelectronics Unit Indian Statistical Institute Kolkata India

   Advanced Computing & Microelectronics Unit Indian Statistical Institute Kolkata India