We propose an electromechanical scheme where the electronic degrees of freedom of boron vacancy color centers hosted by a hexagonal boron nitride nanoribbon are coupled for quantum information processing. The mutual coupling of color centers is provided via their coupling to the mechanical motion of the ribbon, which in turn stems from the local strain. The coupling strengths are computed by performing ab-initio calculations. The density functional theory (DFT) results for boron vacancy centers on boron nitride monolayers reveal a huge strain susceptibility. In our analysis, we take into account the effect of all flexural modes and show that despite the thermal noise introduced through the vibrations one can achieve steady-state entanglement between two and more number of qubits that survives even at room temperature. Moreover, the entanglement is robust against mis-positioning of the color centers. The effective coupling of color centers is engineered by positioning them in the proper positions. Hence, one is able to tailor stationary graph states. Furthermore, we study the quantum simulation of the Dicke-Ising model and show that the phonon superradiance phase transition occurs even for a finite number of color centers. Given the steady-state nature of the proposed scheme and accessibility of the electronic states through optical fields, our work paves the way for the realization of steady-state quantum information processing with color centers in hexagonal boron nitride membranes.
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