Quantum technologies such as quantum sensing, quantum imaging, quantum communications, and quantum computing rely on the ability to actively manipulate the quantum state of light and matter. Quantum emitters, such as color centers trapped in solids, are a useful platform for the realization of elementary building blocks (qubits) of quantum information systems. In particular, the modular nature of such solid-state devices opens up the possibility to connect them into quantum networks and create non-classical states of light shared among many qubits. The function of a quantum network relies on efficient and controllable interactions among individual qubits. In this context, we present a scheme where optically active qubits of differing excitation energies are mutually coupled via a dispersive interaction with a shared mode of an optical cavity. This generally off-resonant interaction is prohibitive of direct exchange of information among the qubits. However, we propose a scheme in which by acoustically modulating the qubit excitation energies it is in fact possible to tune to resonance a pre-selected pair of qubits and thus open a communication channel between them. This method potentially enables fast (∼ns) and parallelizable on-demand control of a large number of physical qubits. We develop an analytical and a numerical theoretical model demonstrating this principle and suggest feasible experimental scenarios to test the theoretical predictions.