  A single electron floating on the surface of a condensed noble-gas liquid or
solid can act as a spin qubit with ultralong coherence time, thanks to the
extraordinary purity of such systems. Previous studies suggest that the
electron spin coherence time on a superfluid helium (He) surface can exceed 100
s. In this paper, we present theoretical studies of the electron spin coherence
on a solid neon (Ne) surface, motivated by our recent experimental realization
of single-electron charge qubit on solid Ne. The major spin decoherence
mechanisms investigated include the fluctuating Ne diamagnetic susceptibility
due to thermal phonons, the fluctuating thermal current in normal metal
electrodes, and the quasi-statically fluctuating nuclear spins of the $^{21}$Ne
ensemble. We find that at a typical experimental temperature about 10 mK in a
fully superconducting device, the electron spin decoherence is dominated by the
third mechanism via electron-nuclear spin-spin interaction. For natural Ne with
2700 ppm abundance of $^{21}$Ne, the estimated inhomogeneous dephasing time
$T_{2}^{*}$ is around 0.16 ms, already better than most semiconductor
quantum-dot spin qubits. For commercially available, isotopically purified Ne
with 1 ppm of $^{21}$Ne, $T_{2}^{*}$ can be $0.43$ s. Under the application of
Hahn echoes, the coherence time $T_{2}$ can be improved to $30$ ms for natural
Ne and $81$ s for purified Ne. Therefore, the single-electron spin qubits on
solid Ne can serve as promising new spin qubits.
