Correcting biased noise using Gottesman-Kitaev-Preskill repetition code with noisy ancilla
Z. Li, Daiqin Su · Physical Review A · 2024
Concatenation of a bosonic code with a qubit code is one of the promising ways to achieve fault-tolerant quantum computation. As one of the most important bosonic codes, the Gottesman-Kitaev-Preskill (GKP) code is proposed to correct small displacement errors in phase space. If the noise in phase space is biased, the square-lattice GKP code can be concatenated with the repetition code that promises a high fault-tolerant threshold to suppress the logical error. In this work, we study the performance of GKP repetition codes with finite-energy ancillary GKP qubits in correcting biased noise. We find that there exists a critical value of noise variance for the ancillary GKP qubit such that the logical Pauli error rate decreases when increasing the code size. Furthermore, one round of GKP error correction has to be performed before concatenating with the repetition code. Our study paves the way for practical implementation of error correction by concatenating the GKP code with low-level qubit codes.