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arXiv:2607.12565 · Quantum Science and Technology

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

Yan Lu, Xiao-Feng Shi

quant-phSubmitted Jul 14, 2026• Announced Jul 15, 2026• 0 citations
arXivHTMLPDF

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~(QFG) 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 $6π/Ω_{\text{m}}$ with $Ω_{\text{m}}$ the maximal Rydberg Rabi frequency. From a product state of three data atom 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, $\cdots$-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.

Journal reference
Quantum Sci. Technol. 11 015048 (2026)
DOI
10.1088/2058-9565/ae34e1
Comments
32 pages, 8 figures

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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~(QFG) 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 6π/Ωm6π/Ω_{\text{m}}6π/Ωm​ with ΩmΩ_{\text{m}}Ωm​ the maximal Rydberg Rabi frequency. From a product state of three data atom 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, ⋯\cdots⋯-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.
We present a novel class of Rydberg-mediated nuclear-spin entanglement in divalent atoms with global laser pulses. First, we show a fast nuclear-spin controlled phase gate of an arbitrary phase realizable either with two laser pulses when assisted by Stark shifts, or with three pulses. Second, we propose to create an electrons–nuclei-entangled state, which is named a super bell state (SBS) for it mimics a large Bell state incorporating three small Bell states. Third, we show a protocol to create a three-atom electrons-nuclei entangled state which contains the three-body W and Green-berger–Horne–Zeilinger (GHZ) states simultaneously. These protocols possess high intrinsic fidelities, do not require single-site Rydberg addressing, and can be executed with large Rydberg Rabi frequencies in a weak, Gauss-scale magnetic field. The latter two protocols can enable measurement-based preparation of Bell, hyperentangled, and GHZ states, and, specifically, SBS can enable quantum dense coding where one can share three classical bits of information by sending one particle.
We propose a scalable protocol in the Rydberg atomic system to generate the Greenberger-Horne-Zeilinger (GHZ) states, where the qubits are encoded on the hyperfine ground levels. Our system is featured with off-resonant driving fields rather than strong Rydberg interaction sufficient for blockade. Closely it can follow the desired nonadiabatic passage during the time evolution and avoid the unwanted transition by imposing the passage-dependent and fast-varying global phase, that serves as an error correction to the universal quantum control. In our protocol, an NNN-qubit GHZ state is prepared in N−1N-1N−1 steps, which is found to be robust against both environmental noise and systematic deviation. Our protocol therefore provides an avenue toward large-scale entanglement, which is essential for quantum information processing and computation based on neutral atoms.
Fast nuclear-spin entangling gates of divalent atoms can be realized with one global laser pulse when ${\mathrm{\ensuremath{\Delta}}}_{\text{Z}}<\mathrm{\ensuremath{\Omega}}$, where ${\mathrm{\ensuremath{\Delta}}}_{\text{Z}}$ is the Zeeman-splitting-dominated frequency difference between the two clock-Rydberg transitions of the two qubit states and $\mathrm{\ensuremath{\Omega}}$ is the maximal Rabi frequency. The condition ${\mathrm{\ensuremath{\Delta}}}_{\text{Z}}<\mathrm{\ensuremath{\Omega}}$ and the sensitivity of Rydberg-state energy to magnetic fluctuation demand the magnetic field to be weak, making the gate compatible with large-scale atomic arrays because weaker magnetic fields can be smoother in a large qubit array. The gate can have a high fidelity for the decoherence of Rydberg states, which limits the gate fidelity and grows with $1/\mathrm{\ensuremath{\Omega}}$, can be mitigated with easily attainable large $\mathrm{\ensuremath{\Omega}}$.
Greenberger-Horne-Zeilinger (GHZ) state is a typical maximally entangled state which is pursued in both fundamental research and emerging quantum technologies. Preparing large-scale GHZ states in lattice spin systems is particularly appealing for quantum advantages, but conventional schemes face great challenges in scalability. Here we propose a universal and scalable scheme to generate large-scale GHZ-like states, which share similar entanglement and metrological properties with standard GHZ states, in lattice spin systems through global Floquet engineering. Our scheme requires only global operations and shows great advantage for large particle number. It is applicable to systems with arbitrary interaction ranges, offering a practical pathway for large-scale implementation of many-body entangled states in various systems.
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The multipartite Greenberger–Horne–Zeilinger (GHZ) states play an important role in large-scale quantum information processing. We utilize the polychromatic driving fields and the engineered spontaneous emissions of Rydberg states to dissipatively drive three- and four-partite neutral atom systems into the steady GHZ states, at the presence of the next-nearest neighbor interaction of excited Rydberg states. Furthermore, the introduction of quantum Lyapunov control can help us optimize the dissipative dynamics of the system so as to shorten the convergence time of the target state, improve the robustness against the spontaneous radiations of the excited Rydberg states, and release the limiting condition for the strengths of the polychromatic driving fields. Under the feasible experimental conditions, the fidelities of three- and four-partite GHZ states can be stabilized at 99.24 % and 98.76 %, respectively.