Abstract
Gottesman-Kitaev-Preskill (GKP) qubit is a promising ingredient for fault-tolerant quantum computation (FTQC) in optical continuous variables due to its advantage of noise tolerance and scalability. However, one of the main problems in the preparation of the optical GKP qubit is the difficulty in obtaining the nonlinearity. Cross-Kerr interaction is one of the promising candidates for this nonlinearity. There is no existing scheme to use the cross-Kerr interaction to generate the optical GKP qubit for FTQC. In this work, we propose a generation method of the GKP qubit by using a cross-Kerr interaction between a squeezed light and a superposition of Fock states. We numerically show that the GKP qubit with the 10 dB can be generated with a mean fidelities of 99.99 and 99.9% at the success probabilities of 2.7 and 4.8%, respectively. Therefore, our method has potential method to generate the optical GKP qubit with a quality required for FTQC when we obtain the sufficient technologies for the preparation of ancillary Fock states and a cross-Kerr interaction.
Highlights
Quantum information processing with continuous variables (CVs) [1,2] has been receiving attentions for a few decades
Our method has the potential to generate the optical GKP qubit with a quality required for fault-tolerant quantum computation (FTQC) when we obtain the sufficient technologies for the preparation of ancillary Fock states and a cross-Kerr interaction
The GKP qubit has the advantages of an error tolerance and scalability towards large-scale quantum computation (QC) with CVs: (1) The GKP qubit is designed to protect against small displacement noise and can achieve the hashing bound of the additive Gaussian noise with a suitable quantum error correcting code [9,10]
Summary
Quantum information processing with continuous variables (CVs) [1,2] has been receiving attentions for a few decades. The GKP qubit has the advantages of an error tolerance and scalability towards large-scale quantum computation (QC) with CVs: (1) The GKP qubit is designed to protect against small displacement noise and can achieve the hashing bound of the additive Gaussian noise with a suitable quantum error correcting code [9,10]. It protects against other types of noise, including noise from finite squeezing during measurementbased QC [11] and photon loss [12].
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