(color online) (a) SEM image of a flux qubit device. The red part is the flux qubit loop. The width and thickness of the wire are 300 nm and 80 nm, respectively. By using different junction parameters, the persistent current I_p in the main loop can vary from 100 nA to 1 μ A. (b) Schematic diagram for the coupling strength simulation. The red part is the flux qubit loop, which has the same size as in panel (a). The box above the flux qubit loop is the NV⁻ ensemble. We simulate the magnetic field distribution by finite element analysis. (c) Simulated results. We calculate gap dependent NV⁻ concentration required to achieve a 10-MHz coupling strength for I_p = 300 nA and I_p = 500 nA, where gap is the distance between bottom surface of NV⁻ ensemble and top surface of flux qubit. The simulated result gives a lower bound of 9.96 × 10¹⁵ cm⁻³ for NV⁻ concentration when I_p is 500 nA and there is no gap between NV⁻ ensemble and flux qubit.