Optomechanical Grid State Encoding for Continuous‐Variable Quantum Information

ABSTRACT

The Gottesman–Kitaev–Preskill state encoding is a promising approach for achieving fault‐tolerant quantum computation due to its resilience to small displacement errors and compatibility with Gaussian operations. In this work, we present a pulsed optomechanical protocol for synthesizing approximate grid‐like states in a macroscopic mechanical oscillator via strong single‐photon nonlinearity. The proposed scheme assumes a momentum‐squeezed mechanical mode as the initial state, followed by two sequential radiation‐pressure pulse interactions and homodyne measurements. The protocol requires two measurement stages, separated by a quarter‐period phase‐space rotation and accompanied by an outcome‐dependent feedback operation. The first sequence generates a one‐dimensional comb in phase space and subsequently converts it into an approximate two‐dimensional lattice after the second measurement. We further examine how finite squeezing, optical loss, and thermal phonon occupation influence the resulting encoding. The heralding probability and logical error rates have also been demonstrated with the measurement outcomes. Our results establish pulsed optomechanics as a viable approach to embedding bosonic error‐correcting codes in mechanical systems, with applications to quantum memories, hybrid transduction, and continuous‐variable architectures.