An Arizona Notary public should notarize the Arizona quitclaim deed
Samples of Notary Stamps 
The state of Arizona, however, does recognize notarization from other states. Therefore, it is not set in stone that an Arizona quitclaim deed can only be notarized in Arizona.
If you are filing the Arizona quitclaim deed from another state or it is inconvenient to visit any of the Arizona notaries within the list below, you may visit any public notary.
It is always best to contact the County Recorder’s Office in the county that you will recording and ask them if they will recognize documents that are notarized by a notary public officials from other states.
Search for a Notary within your county
State of Arizona Notary Search
When you arrive at the Arizona Secretary of State Notary Public System page, scroll down to about the middle of the form and look for “COUNTY.” Plug in your county and then click on “Start Search.”