Single-Period Floquet Control of Bosonic Codes with Quantum Lattice Gates.

Bosonic codes constitute a promising route to fault-tolerant quantum computing. Existing Floquet protocols enable analytical construction of bosonic codes but typically rely on slow adiabatic ramps with thousands of driving periods. In this Letter, we circumvent this bottleneck by introducing an analytical and deterministic Floquet method that directly synthesizes arbitrary unitaries within a single period. The phase-space unitary ensembles generated by our approach reproduce the Haar-random statistics, enabling practical pseudorandom states in continuous-variable systems. We prepare various prototypical bosonic codes from vacuum and implement single-qubit logical gates with high fidelities using quantum lattice gates. By harnessing the full intrinsic nonlinearity of Josephson junctions, quantum lattice gates decompose quantum circuits into primitive operations for efficient continuous-variable quantum computing.