High-threshold fualt-tolerant quantum computation with GKP qubits and realistically noisy devices

To implement fault-tolerant quantum computation with continuous variables, the Gottesman-Kitaev-Preskill (GKP) qubit has been recognized as an important technological element. We have proposed a method to reduce the required squeezing level to realize large scale quantum computation with the GKP qubits [Phys. Rev. X. 8, 021054 (2018)]. Although our method can reduce the required squeezing level to less than 10 dB, which is within the reach of the current experimental technology, we have assumed that the CZ gate and an efficiency of the homodyne detection are ideal. In this work, we show that the required squeezing level is around 10 dB under the realistic assumption that the CZ gate and homodyne detection degrade the squeezing level of the GKP qubits, developing a method to reduce a noise on the GKP qubit by using postselection and maximum-likelihood methods.