An Efficient Method for Cluster State Construction based on Counterfactual Carving in an Optical Cavity

We show how counterfactual carving, a recently developed theoretical proposal to produce high fidelity, multipartite entanglement, could be applied to generate fully-connected resource states for measurement-based quantum computing. For a neutral atom ensemble in an optical cavity, the cavity mode spectrum is shifted differently by each Dicke state of the collective spin. A "source" atom illuminated with multiple tones tuned near resonances of the cavity mode spectrum imparts unique amplitude and phase shifts to the Dicke states dependent on tone strengths and detunings. We develop a simple prescription of tones that produces fully-connected graph states of resource qubits, which can be efficiently merged into cluster states for universal quantum computation. Importantly, the ability to carve many-body entanglement enables resource state creation in a single cavity operation, eliminating the need for the time-consuming, low success probability two-qubit operations typically used to generate the resource state.