State Injection and Syndrome Decoding for Rotated Surface Code in Quantum Computing

Abstract

In this paper, we analyze a syndrome decoding problem that occurs when performing state injection on rotated surface code with distance = 3 and propose a method to solve it. When state injection is performed on the rotated surface code with distance 3, there are some cases that the state of logical qubit becomes $\alpha\vert 0> \mathrm{L}-\upbeta\vert 1> \mathrm{L}$. due to the syndrome decoding problem. In this paper, we analyze the problem and propose an syndrome decoding method for the state injection. In addition, this was verified using quantum simulators.