Low Depth Color Code Circuits with CXSWAP gate

Abstract

We present two new types of syndrome extraction circuits for the color code. Our first construction, which after [M. McEwen, D. Bacon, and C. Gidney, Quantum 7, 1172 (2023)] we call the semi-wiggling color code, promises to mitigate leakage errors by periodically interchanging the roles of bulk data and measurement qubits. The second construction reduces circuit depth relative to [C. Gidney and C. Jones, arXiv:2312.08813 (2023)] by employing the CXSWAP gate instead of CNOT. This optimization leads to $\sim 10\%$ improvement in teraquop footprint under the uniform error model with the physical error rate $p=0.1\%$.