Bosonic Quantum Error Correction with Neutral Atoms in Optical Dipole Traps

TL;DR

This paper explores the theoretical preparation and error correction of GKP bosonic qubits using neutral atoms in optical dipole traps, highlighting the potential of optical lattices for robust quantum encoding.

Contribution

It introduces protocols for GKP qubit encoding in neutral atoms, comparing optical tweezer arrays and lattices, and demonstrates experimental feasibility through numerical simulations.

Findings

Optical lattices offer more flexible control for GKP encoding.

Small anharmonicity and frequency differences aid robust encoding.

Numerical simulations confirm protocol feasibility with realistic parameters.

Abstract

Bosonic quantum error correction codes encode logical qubits in the Hilbert space of one or multiple harmonic oscillators. A prominent class of bosonic codes is that of Gottesman-Kitaev-Preskill (GKP) codes of which implementations have been demonstrated with trapped ions and microwave cavities. In this paper, we investigate theoretically the preparation and error correction of a GKP qubit in a vibrational mode of a neutral atom stored in an optical dipole trap. This platform has recently shown remarkable progress in simultaneously controlling the motional and electronic degrees of freedom of trapped atoms. The protocols we develop make use of motional states and, additionally, internal electronic states of the trapped atom to serve as an ancilla qubit. We compare optical tweezer arrays and optical lattices and find that the latter provide more flexible control over the confinement in the out-of-plane direction, which can be utilized to optimize the conditions for the implementation of GKP codes. Concretely, the different frequency scales that the harmonic oscillators in the axial and radial lattice directions exhibit and a small oscillator anharmonicity prove to be beneficial for robust encodings of GKP states. Finally, we underpin the experimental feasibility of the proposed protocols by numerically simulating the preparation of GKP qubits in an optical lattice with realistic parameters.