Summary: Quantum Computing Stack Exchange will begin the nomination stage for a special election on October 29 to replace one of the current moderators.
For full details of the process, see the announcement on Meta Stack Exchange. The timeline:
During the nomination period, users may nominate themselves and answer any questions that might have been asked on meta.
On November 5, if there are two or more candidates, we'll run an election. If not, I'll simply appoint the candidate. (There's a small chance we'll need to remove a nomination, but I doubt that will come up.)
If there is an election, I'll announce the results on meta on November 13.
(Note for current moderators: there's no need to nominate yourself even though you'll likely get an email saying you should.)
If you have any questions about the process, please stick them in an answer here.