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This is difficult to answer, because I'm not sure what you are getting at. Each state keeps its own criminal records, so if you move to, for instance, Wisconsin, then you will not have a criminal record in Wisconsin.
But, your felony will still be on your record, if anyone goes so far as to check in California. If you get a job that requires checking your background, they will undoubtedly come up with your California felony record. Also, if you apply for a job and you are asked if you have ever been convicted of a felony, you must answer yes.
I would not go so far as to say you have a "clean slate" but you sort-of have a clean slate. Let's put it this way--if you are applying for most jobs, they are not going to do a criminal records check on you. But, some jobs do, and if they do, they will find out.
You are a convicted felon, and as such, have to adhere to Washington's laws regarding voting and possession of firearms.
No one can use someone's record as a reason for searches or investigations. Not in Washington, or anywhere.