  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.
