Surface code design for asymmetric error channels

Surface codes are quantum error correcting typically defined on a 2D array of qubits. A [dx, dz] surface code design is being introduced, where dx(dz) represents the distance for bit (phase) correction, motivated by fact that severity flip and phase errors in physical system asymmetric. We present pseudo-threshold threshold values proposed asymmetric channels presence various degrees asymmetry Pauli X ^ , Y $\text{Pauli}\,\hat{X},\,\hat{Y}$ Z $\text{and}\,\hat{Z}$ depolarisation channel. demonstrate compared to symmetric codes, our can provide almost double rates while requiring less than half number qubits increasing Our results show low degree asymmetry, it advantageous increase dx along with dz. However, as channel increases, higher obtained dz when kept constant at value. Additionally, we also advantage begins saturate any possible continued be increased.