Optical Gottesman-Kitaev-Preskill qubit generation via approximate squeezed coherent state superposition breeding

TL;DR

This paper introduces a new breeding method for optical GKP qubits that significantly increases success probability while maintaining high fidelity, advancing practical quantum error correction.

Contribution

It proposes a novel breeding scheme using generalized photon subtraction and a single homodyne measurement to improve success rates of optical GKP qubit generation.

Findings

Success probabilities ≥ 10^{-5}, two orders higher than previous methods.

States with error-correction capabilities up to 10 dB squeezing.

Maintains high fidelity comparable to existing high-quality GKP qubits.

Abstract

Gottesman-Kitaev-Preskill (GKP) qubits, known for their exceptional error-correction capabilities, are highly coveted in quantum computing. However, generating optical GKP qubits has been a significant challenge. Measurement-based methods, where a portion of entangled squeezed vacuum modes are measured with photon number resolving detectors heralding a desired state in the undetected modes, have emerged as leading candidates for optical GKP qubit generation due their minimal resource requirements. While the current measurement-based methods can produce high-quality GKP qubits, they suffer from low success probabilities limiting experimental realization. The heart of the problem lies in the duality of photon number resolving measurements, being both the source of nonlinearity needed to generate quality GKP qubits and the component driving down their probability of successful production. Our method, breeding approximate squeezed coherent state superpositions created by generalized photon subtraction, overcomes this problem by supplementing two photon number resolving measurements with a single high success probability homodyne measurement. This scheme achieves success probabilities $\geq 10^{-5}$, two orders of magnitude higher than strictly photon number resolving measurement-based methods, while still producing states with high fidelity, possessing error-correction capabilities equivalent to up to a 10 dB squeezed GKP qubit. This breakthrough significantly advances the practical use of the optical GKP qubit encoding.