Lowering Connectivity Requirements For Bivariate Bicycle Codes Using Morphing Circuits

TL;DR

This paper introduces a new family of Bivariate Bicycle codes with reduced qubit connectivity requirements, using morphing circuits, while maintaining performance, and provides a framework for designing such circuits for group algebra codes.

Contribution

It generalizes morphing circuit design to lower connectivity in BB codes and offers a framework for applying this to two-block group algebra codes.

Findings

Reduced qubit connectivity from six to five in BB codes.

Maintained numerical performance with lower connectivity.

Framework for designing morphing circuits for group algebra codes.

Abstract

In Ref. [1], Bravyi et al. found examples of Bivariate Bicycle (BB) codes with similar logical performance to the surface code but with an improved encoding rate. In this work, we generalize a novel parity-check circuit design principle called morphing circuits and apply it to BB codes. We define a new family of BB codes whose parity check circuits require a qubit connectivity of degree five instead of six while maintaining their numerical performance. Logical input/output to an ancillary surface code is also possible in a biplanar layout. Finally, we develop a general framework for designing morphing circuits and present a sufficient condition for its applicability to two-block group algebra codes [1] S. Bravyi, A. W. Cross, J. M. Gambetta, D. Maslov, P. Rall, and T. J. Yoder, Nature 627, 778 (2024).