Do what I do when I'm done with a job. Just stop going, they'll get the hint after a few days & hire someone else.
Everyone that I have known to give a two week notice has been let go early. So why bother? The majority is correct here, you work in a grocery store. Even if you were head manager, you can be replaced easily. They won't miss you. If you ever have to get another job after the one you have lined up, just give them the info. No one will be working at the store you work at now by that time anyway. They won't remember you.