Surface code design for asymmetric error channels

IET Quantum Communication

article

Utkarsh Azad¹  Aleksandra Lipińska⁴  Shilpa Mahato⁵  Rijul Sachdeva⁶  Debasmita Bhoumik⁸  Ritajit Majumdar⁸ 

[1] Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology;Center for Quantum Science and Technology, International Institute of Information Technology;Xanadu;Faculty of Mathematics and Computer Science, Jagiellonian University;Department of Physics, Indian Institute of Technology Dhanbad;Jülich Supercomputing Center;RWTH Aachen University;Advanced Computing & Microelectronics Unit, Indian Statistical Institute

关键词: asymmetric noise model;    quantum error correction;    surface codes;   

DOI  :  10.1049/qtc2.12042

学科分类：环境科学（综合）

来源: Wiley

【 摘 要 】

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 Pauli ◂,▸ X ^ , Y ^ $ext{Pauli},hat{X},,hat{Y}$ , and Z ^ $ext{and},hat{Z}$ 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.

【 授权许可】

CC BY|CC BY-ND|CC BY-NC|CC BY-NC-ND