Bunny Codes: Broadening Superconducting Quantum Error Correction Capability through Advanced Control Engineering

Abstract:Drawing on advances in superconducting qubit control schemes that unlock enriched native gate sets at the hardware level, we systematically examine how harnessing this enlarged physical two-qubit gate pool---specifically CNOT and CXSWAP---streamlines syndrome extraction for certain qLDPC codes with nonlocal stabilizers. Through an exhaustive search, we discover a set of qLDPC codes with various stabilizer weights and distances that can be implemented on the two-dimensional nearest-neighbor qubit connectivity native to superconducting hardware while achieving performance equivalent to that of the direct CNOT implementation requiring long-range interactions. We refer to those codes as Bunny codes. Across all code distances we examine, the best Bunny codes with weight-6 stabilizers in periodic boundary conditions have a code rate approximately $3\times$ that of the toric code; when converted to open boundary conditions, they retain an approximately $2\times$ code rate advantage over the rotated surface code. In circuit-level simulation, we find that some Bunny codes exhibit logical error rates an order of magnitude lower than toric codes with comparable code rates. Our results demonstrate that high-performance quantum error correction can be achieved using an expanded gate set rather than long-range couplers, thereby significantly reducing hardware complexity.

20 pages, 14 figures. Updated data tables

arXiv:2606.22853 [quant-ph]

(or arXiv:2606.22853v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2606.22853 Focus to learn more arXiv-issued DOI via DataCite

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