Logic-qubit CNOT gates in decoherence-free subspaces assisted by the nitrogen-vacancy center

Employing an optical microcavity interacting with a nitrogen-vacancy (NV) center with excellent optical performance and scalability, two logic-qubit controlled-not (CNOT) gates in decoherence-free subspaces (DFSs) are successfully constructed against collective-rotating noise and collective-dephasing noise, respectively. The circuit has a heralded function that can filter out incorrect components. Furthermore, a waveform corrector (WFC) is adopted to balance the amplitude of two components in different spatial modes, thereby achieving high fidelity.