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