Counterdiabatic transfer of a quantum state in a tunable Heisenberg spin chain via the variational principle

We present a couple of counterdiabatic (CD) schemes for a rapid and high-fidelity transfer of quantum state across a one-dimensional spin chain, between two weakly coupled external qubits at each end. Employing the effective low-energy Hamiltonian of the system, we first construct the optimal CD terms based on the variational principle and then put forward two experimentally feasible shortcuts, which only need to manipulate couplings between the external qubits and chain. Compared to traditional adiabatic protocol, the resulting schemes allow a drastic increase in state-transfer fidelity in a short time. Furthermore, numerical simulation demonstrates that our speed-up protocols hold robustness against the imperfections of control fields and evolution time. The proposed schemes may be applicable to fast quantum-information transport in various spin-based physical systems.