That depends on whether or not you actually signed a legally binding and enforceable contract or not.

If you are not under contract, the amount of notice you are legally required to give is zero. You can call up and say, "Boss, I'm not coming in today, or ever again." You can say as you are walking out the door one night, "Oh, btw, today was my last day." No notice whatsoever is required by law.

If you signed an actual contract that specifies that you must give x amount of notice, you can still walk out the door with no notice but your employer *may* be able to take legal action against you.

An employee handbook is rarely considered a legally binding contract. However, you would need to show it to a California attorney to be certain.

At-will is the default. It doesn't matter whether the employer said so or not; you're at-will unless you signed something that says you're not.