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Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study

H. Bombin·M. A. Martin-Delgado
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Abstract

We study the resources needed to construct topological 2D stabilizer codes as a way to estimate in part their efficiency and this leads us to perform a comparative study of surface codes and color codes. This study clarifies the similarities and differences between these two types of stabilizer codes. We compute the error correcting rate $C:=n/d^2$ for surface codes $C_s$ and color codes $C_c$ in several instances. On the torus, typical values are $C_s=2$ and $C_c=3/2$, but we find that the optimal values are $C_s=1$ and $C_c=9/8$. For planar codes, a typical value is $C_s=2$, while we find that the optimal values are $C_s=1$ and $C_c=3/4$. In general, a color code encodes twice as much logical qubits as a surface code does.

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H. Bombin, M. A. Martin-Delgado. 2007-03-29. Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study. https://doi.org/10.1103/physreva.76.012305

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