Generating Gottesman-Kitaev-Preskill qubit using a cross-Kerr interaction between a squeezed light and Fock states in optics

TL;DR

This paper proposes a novel method to generate GKP qubits using cross-Kerr interaction between squeezed light and Fock states, achieving high fidelity suitable for fault-tolerant quantum computing in optics.

Contribution

It introduces a new scheme for optical GKP qubit generation leveraging cross-Kerr interaction, addressing the challenge of nonlinearity in quantum state preparation.

Findings

Achieves GKP qubit with 10 dB squeezing and high fidelity (99.99%)

Success probabilities of 2.7% and 4.8% for different fidelities

Potential for scalable fault-tolerant quantum computation in optics

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.