Parallel-path implementation of nonadiabatic geometric quantum gates in a decoherence-free subspace with nitrogen-vacancy centers

We propose a scheme for nonadiabatic noncyclic geometric quantum computation in a decoherence-free subspace (DFS). The physical system we used is a cavity quantum electrodynamics system consisting of nitrogen-vacancy (NV) centers in diamond and a whispering-gallery-mode (WGM) microresonator. This scheme not only has the feature of DFSs insensitive to decoherence, but also has the advantage of nonadiabatic noncyclic geometric quantum computation which has the built-in noise-resilience geometric feature and further enhances the robustness due to the ability beyond the limitation of the cyclic condition. An unconventional two-qubit phase gate in DFS has been realized in one step with our parallel protocol, which can largely shorten the computation time and the system error caused by decoherence. In addition, a scheme to realize a parallel process of two evolution paths is put forward to achieve the distribution quantum computation of two WGM microresonators containing a NV center in each. Our scheme may provide a promising way towards the practical realization of high-fidelity geometric quantum computation with the features of a DFS, geometric phase, and parallel implementation process.