Cavity-mediated long-range interaction for fast multiqubit quantum logic operations

Interactions among qubits are essential for performing two-qubit quantum logic operations. However, nature gives us only nearest neighbor interactions in simple and controllable settings. Here we propose a strategy to induce interactions among two atomic entities that are not necessarily neighbors of each other through their common coupling with a cavity field. This facilitates fast multiqubit quantum logic operations through a set of two-qubit operations. Using its explicit position dependence, this interaction can be employed for simulation of quantum spin systems. The ideas presented here are applicable to various quantum-information proposals for atom-based qubits such as trapped ions, atoms trapped in optical cavities, and optical lattices.