Analysis of surface code under the restricted number of CNOT gates

To date, the surface code has become a promising candidate for quantum error correcting codes because of its high threshold, nearest gate operations and low weight stabilizers. Here, we assume that the number of CNOT gates is restricted because of the quantum crosstalk due to residual inter-qubit coupling or max channels per pulse gate. We thus calculated the effective physical error rate in this case and determine the surface code distance accordingly. The optimal code distance was obtained based on the logical error rate performance estimation of the surface code for some T1 and T2 time.