Parity-gate-based quantum information processing in decoherence-free subspace with nitrogen-vacancy centers

• The logical qubits are encoded in DFS that immune to collective-dephasing noise.
• The fragile single-photon-resource is replaced by the robust coherent pulse resource.
• The proposed PCG can be used in other quantum information processing tasks.

We propose a parity-check gate (PCG) for logical qubits encoded in decoherence-free subspace (DFS) by the coherent optical pulse input–output process with nitrogen-vacancy (NV) centers fixed on the surface of microtoroidal resonators (MTRs) with quantized whispering-gallery modes (WGMs). Using the proposed PCG, we achieve controlled phase flip (CPF) gate, |χ〉|χ〉 state generation, and multipartite entanglement purification. The present schemes combine the advantages of the robustness of coherent pulse and the immunity to the dephasing noise of the DFS. The performances of these schemes are also analyzed, which shows that all the schemes works well in the low-Q cavity regime and are feasible under the current experimental technology.