2025/04/25 by Arnault, François, Gaborit, Philippe, Saussay, Nicolas · 1 citation
#FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2504.18360
Surface codes have historically been the dominant choice for quantum error correction due to their superior error threshold performance. However, recently, a new class of Generalized Bicycle (GB) codes, constructed from binary circulant matrices with three non-zero elements per row, achieved comparable performance with fewer physical qubits and higher encoding efficiency. In this article, we focus on a subclass of GB codes, which are constructed from pairs of binary circulant matrices with two non-zero elements per row. We introduce a family of codes that generalizes both standard and optimized Kitaev codes for which we have a lower bound on their minimum distance, ensuring performance better than standard Kitaev codes. These codes exhibit parameters of the form [| 2n , 2, ≥ √(n) |] where n is a factor of 1 + d2 . For code lengths below 200, our analysis yields 21 codes, including 7 codes from Pryadko and Wang's database, and unveils 14 new codes with enhanced minimum distance compared to standard Kitaev codes. Among these, 3 surpass all previously known weight-4 GB codes for distances 4, 8, and 12.