Rydberg quantum computation with nuclear spins in two-electron neutral atoms

Abstract

Alkaline-earth-like~(AEL) atoms with two valence electrons and a nonzero nuclear spin can be excited to Rydberg state for quantum computing. Typical AEL ground states possess no hyperfine splitting, but unfortunately a GHz-scale splitting seems necessary for Rydberg excitation. Though strong magnetic fields can induce a GHz-scale splitting, weak fields are desirable to avoid noise in experiments. Here, we provide two solutions to this outstanding challenge with realistic data of well-studied AEL isotopes. In the first theory, the two nuclear spin qubit states $|0⟩$ and $|1⟩$ are excited to Rydberg states $|r⟩$ with detuning $\Delta$ and 0, respectively, where a MHz-scale detuning $\Delta$ arises from a weak magnetic field on the order of 1~G. With a proper ratio between $\Delta$ and $\Omega$, the qubit state $|1⟩$ can be fully excited to the Rydberg state while $|0⟩$ remains there. In the second theory, we show that by choosing appropriate intermediate states a two-photon Rydberg excitation can proceed with only one nuclear spin qubit state. The second theory is applicable whatever the magnitude of the magnetic field is. These theories bring a versatile means for quantum computation by combining the broad applicability of Rydberg blockade and the incomparable advantages of nuclear-spin quantum memory in two-electron neutral atoms.

18 pages, 5 figures

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• Quantum logic and entanglement by neutral Rydberg atoms: methods and fidelity
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• Unselective ground-state blockade of Rydberg atoms for implementing quantum gates
• Hyperentanglement of divalent neutral atoms by Rydberg blockade
• Coherence-preserving cooling of nuclear spin qubits in a weak magnetic field
• Fast nuclear-spin gates and electrons-nuclei entanglement of neutral atoms in weak magnetic fields
• Fast nuclear-spin entangling gates compatible with large-scale atomic arrays
• Coherence enhancement of Rydberg polaritons
• Fast measurement-based generation of large-scale Greenberger-Horne-Zeilinger state with atomic nuclear-spin qubits