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

Generating large-scale Greenberger-Horne-Zeilinger (GHZ) states is a critical challenge for quantum technologies like quantum key distribution and secret sharing. Current methods often struggle with scalability because they require complex, long-range interactions between qubits. This paper addresses the need for a scalable, efficient method to prepare these states in free-space atomic arrays.

The authors introduce a four-qubit "quantum ferromagnetic gate" (QFG) that imprints a pi-phase on specific state components, analogous to the alignment of magnetic moments in a ferromagnet. By utilizing the nuclear-spin qubits of alkaline-earth-like atoms (such as 171Yb), the protocol benefits from near-degenerate Zeeman substates, allowing a single Rydberg laser field to excite both qubit states simultaneously. The generation process uses a "gluing circuit" that combines smaller GHZ states with an ancilla atom and projective measurements to build up to 243-qubit states or larger.

The study demonstrates that the QFG can be realized with high fidelity using Rydberg-mediated interactions. By iteratively applying the gluing circuit—which involves one QFG, two single-qubit gates, and a projective measurement—the protocol can deterministically scale from a 3-qubit GHZ state to 9, 27, 81, and 243-qubit states. The authors analyze the impact of fundamental errors, such as Rydberg-state decay and blockade leakage, and conclude that current experimental techniques in tweezer arrays are sufficient to support this large-scale entanglement.

This work provides a viable roadmap for creating large-scale entangled states in neutral-atom quantum computers. By reducing the complexity of the required gate operations and leveraging the unique properties of nuclear-spin qubits, the proposed protocol offers a path toward overcoming the scalability bottlenecks that currently limit the size of GHZ states in experimental quantum systems.