Local Counterdiabatic Driving for Jaynes-Cummings Lattices

Jaynes-Cummings (JC) lattices, formed by connecting quantum two-level systems with cavities, have been extensively studied for their role in polariton many-body states and multipartite entanglement. While adiabatic evolution has been explored to generate these many-body states, its dependence on long timescales makes it vulnerable to decoherence. In this work, we propose a scheme that employs local counterdiabatic (CD) driving for rapid and high-fidelity state preparation in JC lattices. The exact CD Hamiltonian for this system includes nonlocal interactions between qubits and cavities at distant sites, posing a challenge for practical implementation. By exploiting the symmetries of the eigenstates under both periodic and open boundary conditions, we derive a local CD Hamiltonian that replicates the dynamics of the exact CD Hamiltonian, as confirmed by our numerical simulations. Additionally, we demonstrate that this method enables the high-fidelity preparation of multipartite W-states. We also discuss the implementation and decoherence challenges of this scheme in superconducting quantum devices.