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We propose an electromechanical scheme where the electronic degrees offreedom of boron vacancy color centers hosted by a hexagonal boron nitridenanoribbon are coupled for quantum information processing. The mutual couplingof color centers is provided via their coupling to the mechanical motion of theribbon, which in turn stems from the local strain. The coupling strengths arecomputed by performing ab-initio calculations. The density functional theory(DFT) results for boron vacancy centers on boron nitride monolayers reveal ahuge strain susceptibility. In our analysis, we take into account the effect ofall flexural modes and show that despite the thermal noise introduced throughthe vibrations one can achieve steady-state entanglement between two and morenumber of qubits that survives even at room temperature. Moreover, theentanglement is robust against mis-positioning of the color centers. Theeffective coupling of color centers is engineered by positioning them in theproper positions. Hence, one is able to tailor stationary graph states.Furthermore, we study the quantum simulation of the Dicke-Ising model and showthat the phonon non-equilibrium phase transition occurs even for a finitenumber of color centers. Given the steady-state nature of the proposed schemeand accessibility of the electronic states through optical fields, our workpaves the way for the realization of steady-state quantum informationprocessing with color centers in hexagonal boron nitride membranes.

Strain induced coupling and quantum information processing with hexagonal boron nitride quantum emitters