Fast measurement-based generation of large-scale Greenberger–Horne–Zeilinger state with atomic nuclear-spin qubits

Abstract Large-scale Greenberger–Horne–Zeilinger (GHZ) state is useful for quantum technologies but difficult to be prepared. Here, we propose fast measurement-based preparation of large-scale GHZ states by a four-qubit quantum phase gate with nuclear-spin qubits of alkaline-earth-like atoms, which is named as quantum ferromagnetic gate due to its analogy to the alignment of molecular magnetic moments in a classical magnet. A high-fidelity Rydberg-mediated QFG can be realized in a time of 6 π / Ω m with Ω m the maximal Rydberg Rabi frequency. From a product state of three data atoms and one ancilla atom, a gluing circuit with one QFG, two single-qubit gates, and a projective measurement of the ancilla can generate a 3-qubit GHZ state, and repetition of this gluing circuit can lead to 9, 27, 81, 243 , … -qubit GHZ states. Analyses based on currently available techniques show that a 243-qubit GHZ state is realizable, and more qubits can be entangled with higher detection fidelity.