Preparation of Arbitrary High-Fidelity Decoherence-Free States for a Four-Qubit Hybrid System via Whispering-Gallery-Mode Microresonator

With the assistance of the practical nonlinear interaction of a nitrogen-vacancy (NV) center coupled with whispering-gallery-mode (WGM) microresonator, a heralded preparation protocol of four-qubit hybrid decoherence-free states (logical qubits) is presented, where a single logical qubit encoded on the state of the hybrid system composed of two polarization photons and two NV centers is fully protected against collective decoherence. Compared with the three-qubit decoherence-free states, the four-qubit decoherence-free states have higher dimensions, stronger collective decoherence resistance, richer quantum coherence and higher fault tolerance. For an ideal photon-NV interaction, the efficiencies and fidelities of the hybrid decoherence-free states can, in principle, be close to unity. Otherwise, being directed against a nonideal interaction, the two error-heralded quantum blocks of the preparation process make their fidelities near-perfect at the expense of slight reductions of their efficiencies. Moreover, this hybrid decoherence-free states work in a heralded way and may be experimentally feasible with current technique on regulating the NV-WGM microresonator system.