Generation of GKP (Gottesman - Kitaev - Preskill) States Using Shaken Lattices

propose an experimental project to develop a highly optimized control protocol for generating Gottesman-Kitaev-Preskill (GKP) states in ultracold atoms, with a particular focus on arrays of single atoms trapped in deep optical lattice potentials. Fast, low-error qubit operations are needed for fault-tolerant quantum information processing to avoid errors. Quantum systems with high physical error rates need error-correcting codes. These codes use a bosonic oscillator or logical qubit with multiple physical qubits to encode information in a larger state space. Gottesman-Kitaev-Preskill (GKP) states excel in error-correction and cluster-state quantum computing. Encoded qubit states differ by half the spacing period in GKP states, allowing perfect error correction for displacements up to a quarter of the inter-delta spacing. he experiment will progress towards achieving Bose-Einstein Condensation (BEC), providing a degenerate quantum gas as the foundation for the GKP state preparation. The combination of BEC with advanced optical control will enable the fine-tuning of atom interactions and the precise manipulation required for GKP state generation. The experimental setup, beginning with MOT and progressing through to BEC, lays the groundwork for implementing the proposed control protocols, ensuring high fidelity and stability in GKP state generation. This holistic approach not only advances the technical capabilities in quantum state preparation but also addresses fundamental challenges in quantum error correction.