Lowering Connectivity Requirements For Bivariate Bicycle Codes Using Morphing Circuits

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).

arXiv comment29 pages, 14 figures, 9 tables, minor edits based on referee comments and journal length requirements

References in corpus (11)

• Fault-tolerant quantum computation by anyons
• Improved Simulation of Stabilizer Circuits
• Surface code quantum computing by lattice surgery
• High-threshold and low-overhead fault-tolerant quantum memory
• Stim: a fast stabilizer circuit simulator
• Decoding Across the Quantum LDPC Code Landscape
• Quantum "hyperbicycle" low-density parity check codes with finite rate
• Low-overhead fault-tolerant quantum computing using long-range connectivity
• Hyperbolic and Semi-Hyperbolic Surface Codes for Quantum Storage
• Relaxing Hardware Requirements for Surface Code Circuits using Time-dynamics
• Code Deformation and Lattice Surgery Are Gauge Fixing

Cited by in corpus (6)

• Generalized toric codes on twisted tori for quantum error correction
• LUCI in the Surface Code with Dropouts
• Coprime Bivariate Bicycle Codes and Their Layouts on Cold Atoms
• Symmetry-enriched topological order and quasifractonic behavior in ${\mathbb{Z}}_N$ stabilizer codes
• A dynamic circuit for the honeycomb Floquet code
• Logical operations with a dynamical qubit in Floquet-Bacon-Shor code