Surface version of two-layer generalized-bicycle codes

ORAL

Abstract

Generalized bicycle (GB) ansatz gives short quantum LDPC codes with some of the best parameters [1,2]. Recently, Bravyi et al constructed several low-overhead GB codes with stabilizer generators of weight 6, a feasible implementation as local codes in a two-layer "toric" geometry, and pseudo-thresholds comparable to those of the surface codes [2]. In this work we give a general prescription for constructing "surface" versions of GB codes which do not require periodic boundary conditions. We construct several families of multi-qubit-encoding few-layer surface GB codes, calculate their parameters, design syndrome measurement circuits, and simulate their performance under circuit noise using BP+OSD decoder.

* This work was supported in part by the APS M. Hildred Blewett Fellowship (HKL) and the NSF Division of Physics via the grant 2112848 (LPP).

–

Publication: [1] R. Wang and L. P. Pryadko ``Distance Bounds for Generalized Bicycle Codes," Symmetry 14 (2022) 7, 1348.
[2] H. Lin and L. P. Pryadko ``Quantum two-block group algebra codes,'' arXiv:2306.16400
[3] S. Bravyi, A. W. Cross, J. M. Gambetta, D. Maslov, P. Rall, and T. J. Yoder ``High-threshold and low-overhead fault-tolerant
quantum memory,'' arXiv:2308.07915

Presenters

  • Renyu Wang

    University of California, Riverside

Authors

  • Renyu Wang

    University of California, Riverside

  • Hsiang Lin

    University of California, Riverside

  • Xingrui Liu

    University of California, Riverside

  • Leonid P Pryadko

    University of California, Riverside