Quantum state engineering in three-level systems via Lewis-Riesenfeld invariants

Coherent manipulation of three-level systems is of critical significance to quantum information processing. Here, we propose a scheme to achieve quantum state engineering in arbitrary three-level systems, in which the controlling Hamiltonian can be inversely engineered based on Lewis-Riesenfeld invariants and a gauge transformation. With well-designed control pulses, the three-level system continually evolves from the initial state to a desired final state in one step. The proposed scheme allows diverse optimizations, which gives it a significant advantage in robustness and fidelity over the commonly used resonant-pulse multistep method. The scheme can also be extended to produce multiqubit entangled states provided with a similar state subspace. In a particular application, we demonstrate numerically that our protocol can reliably and robustly prepare qutrit states as well as three-qubit entangled W states within superconducting circuits.