Rectangular surface code under biased noise

Abstract To date, the surface code has become a promising candidate for quantum error correcting codes because it achieves high threshold and is composed of only nearest gate operations low-weight stabilizers. Here, we have exhibited that logical failure rate can be enhanced by manipulating lattice size they show an enormous improvement in number physical qubits noise model where dephasing errors dominate over relaxation errors. We estimated terms rate. When was high, parameter estimation method applied, when low, most frequently occurring cases were considered. By using minimum weight perfect matching decoding algorithm, obtained optimal minimizing to achieve required rates bias are provided .