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

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 $|0\rangle$ and $|1\rangle$ are excited to Rydberg states $|r\rangle$ 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 $|1\rangle$ can be fully excited to the Rydberg state while $|0\rangle$ 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.