Engineering Fault-tolerant Bosonic Codes with Quantum Lattice Gates

Abstract: Bosonic codes enable the protection and correction of quantum information in a single continuous variable system. In this talk, I will introduce a systematic framework to engineer bosonic code states for fault-tolerant quantum computing based on Floquet Hamiltonian engineering [PRL132, 023602 (2024)]. We construct the target Hamiltonian directly from the target state and engineer the codes states with an adiabatic ramp protocol. We introduce a new universal set of quantum lattice gate composed of only one type of gate element, and develop a systematic decomposition of complex code state preparation and transformation processes into sequences of quantum lattice gates. Our proposal is particularly well-suited for superconducting circuit architectures with Josephson junctions, where the full nonlinearity of Josephson junction potential is harnessed as a quantum resource.