Controlled phase gate and Grover’s search algorithm on two distant NV-centers assisted by an NAMR

We propose a scheme to construct a controlled phase gate on two distant nitrogen-vacancy centers (NV-centers) assisted by a quantized nanomechanical cantilevel resonator (NAMR). Unlike the previous work to complete the gate in the dispersive regime to let NV-centers detune with the NAMR largely, our gate is completed by using resonant operations between NV-centers and the NAMR, and single-qubit operations on the NV-center, which let the gate to be achieved within a short time with a high fidelity. To study the performance of the gate for universal quantum computation, we simulate a two-qubit Grover’s search algorithm on the NV-centers with a fidelity of $$98.46\%$$.