It will depend upon what state your provisional permit is issued in and the restrictions of that state if you can drive without adult supervision. You will need to check with your state's licensing agency, which is usually part of the Department of Motor Vehicles.

In some states if your are 18 or over and have a provisional or learner's permit the restrictions are less than if you are under 18. For example, in Maryland upon becoming 18 a provisional license holder is no longer bound by time restrictions and may drive at any hour.

In Oregon provisional licensed or permitted drivers have restrictions on them, including being required to be accompanied by a licensed driver who is at least 25 years old. But the restrictions only apply until you are 18 or you have had your provisional license for one year; whichever comes first. 

Check with your DMV before driving without supervision in case your state still requires you to have an older licensed adult with you during this phase of the graduated licensing process.