Entangling distant systems via universal nonadiabatic passage

In this paper, we derive universal nonadiabatic passages in a general $M+N$-dimensional discrete system, where $M$ and $N$ denote the degrees of freedom for the assistant and working subspaces, respectively, that could be separated by rotation or energy and coupled through driving. A systematic method is provided to construct parametric ancillary bases by the von Neumann equation with the time-dependent system Hamiltonian. The resulting universal passages set up connections between arbitrary initial and target states. In applications, a transitionless dynamics can be formulated to entangle distant qubits, as a crucial prerequisite for practical quantum networks. Using tunable longitudinal interaction between distant qubits and driving frequency, the superconducting qubits can be prepared from the ground state to the single-excitation Bell state with a fidelity as high as $\mathcal{F}=0.997$ and be further converted to the double-excitation Bell state with $\mathcal{F}=0.982$. Moreover, our protocol is extended to generate the Greenberger-Horne-Zeilinger state for an $N$-qubit system with $N$ steps. Our work develops a full-fledged theory for nonadiabatic state engineering, which is flexible in target selection and robust against both external noises and systematic errors in quantum information processing.