Lowering Connectivity Requirements For Bivariate Bicycle Codes Using Morphing Circuits

• URL: http://arxiv.org/abs/2407.16336v2
• Date: Tue, 20 Aug 2024 09:58:06 GMT
• Title: Lowering Connectivity Requirements For Bivariate Bicycle Codes Using Morphing Circuits
• Authors: Mackenzie H. Shaw, Barbara M. Terhal,
• Abstract summary: We introduce a novel parity-check circuit design principle that we call morphing circuits. We show how to perform logical input/output circuits to an ancillary rotated surface code using morphing circuits. The new codes perform at least as well as those of Ref. [1] under uniform circuit-level noise.
• Score: 0.7980273012483661
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recently, Bravyi et al. [1] proposed a set of small quantum Bivariate Bicycle (BB) codes that achieve a similar circuit-level error rate to the surface code but with an improved encoding rate. In this work, we generalise a novel parity-check circuit design principle that we call morphing circuits (first introduced in [2]) and apply this methodology to BB codes. Our construction generates a new family of BB codes -- including a new $[[144,12,12]]$ "gross" code -- whose parity check circuits require a qubit connectivity of degree five instead of six. Intriguingly, each parity check circuit requires only 6 rounds of CNOT gates -- one fewer than in Ref. [1] -- even though our new codes have weight-9 stabilisers. We also show how to perform logical input/output circuits to an ancillary rotated surface code using morphing circuits, all within a biplanar layout. The new codes perform at least as well as those of Ref. [1] under uniform circuit-level noise when decoded using BP-OSD. 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). [2] C. Gidney and C. Jones, New circuits and an open source decoder for the color code (2023), arXiv:2312.08813.

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