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Published on: April 15, 2015
Lowering Connectivity Requirements for Bivariate Bicycle Codes Using Morphing Circuits
Mackenzie H Shaw1, Barbara M Terhal1
1Delft University of Technology, QuTech, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands and Delft Institute of Applied Mathematics, Mekelweg 4, 2628 CD Delft, The Netherlands.
Abstract:
In reference Bravyi et al., [Nature (London) 627, 778 (2024)NATUAS0028-083610.1038/s41586-024-07107-7], 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 or 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.
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