| （英） |
Color codes are promising quantum error correction (QEC) codes because they have an advantage against surface codes in that all Clifford gates can be implemented transversally. However, color codes have a drawback of low thresholds under circuit-level noise compared to those of surface codes. Here, we propose a method to suppress the impact of errors and improve the thresholds by optimizing weights of decoders using flag qubits and reducing the circuit depth of the syndrome measurement circuit using cat states. In numerical simulations, we improve the threshold of the (4.8.8) color code under standard circuit-level noise from 0.14% to around 0.27%, which is calculated by using the integer programming decoder. Moreover, the achieved logical error rates at low physical error rates are almost one order of magnitude lower than those achieved by the existing QEC schemes. This method can also be applied to other weight-based decoders, making the color codes more promising for the candidate of experimental implementation of QEC. Furthermore, one can utilize this approach to improve the threshold of wider classes of QEC codes, such as high-rate quantum LDPC codes. |