Cavity polariton blockade for non-local entangling gates with trapped atoms

We propose a scheme for realizing multi-qubit entangled W-state and non-local CZ and gates via a cavity polariton blockade mechanism with a system of atomic qubits coupled to a common cavity mode. The polariton blockade is achieved by tuning the system, an qubit register, such that no two atoms are simultaneously excited to the qubit excited state, and there is an effective coupling only between the ground state and a singly-excited W state of the qubit register. The control step requires only an external drive of the cavity mode and a global qubit pulse and no individual qubit addressing. We analytically obtain the state preparation error upper bound for an qubit W state which scales as where C is the single particle cooperativity. We additionally show the application of the polariton blockade mechanism in realizing a non-local CZ and gate by using a different set of computational qubit states, and characterize the gate infidelity upper bounds which scale as .