Engineering bosonic codes with quantum lattice gates

Abstract Bosonic codes offer a hardware-efficient approach to encoding and protecting quantum information with a single continuous-variable bosonic system. However, previous quantum gates lack analytical methods for decomposing quantum circuits and require complex implementation techniques. In this paper, we introduce a universal quantum gate set composed of only one type of gate element, which we call the quantum lattice gate. We develop a systematic analytical framework for engineering bosonic code states based on Floquet Hamiltonian engineering, where the target Hamiltonian is constructed directly from the given target state(s), and apply our method to single code state preparation, code space embedding, and transformation. We also explore the application of our method to autonomous quantum error correction against single-photon loss with four-legged cat codes. Our proposal is particularly well-suited for superconducting circuit architectures with Josephson junctions, where the full nonlinearity of the Josephson junction potential is harnessed as a quantum resource and the quantum lattice gate can be implemented on a sub-nanosecond timescale.