Rather than paying people more to flip burgers, I think it's better policy to top them off with cash and incentivize them to earn more money by getting better jobs.
The EIC is a form of Negative Income Tax that was originated by Milton Friedman. http://www.econlib.org/library/Enc1/NegativeIncomeTax.html
Adding a state-level EIC would be considerably more administratively complex for California than changing the level of the existing minimum wage -- which, even granting for the sake of argument that such an approach would be desirable ignoring administrative costs, might strongly disfavor that approach.
> The EIC is a form of Negative Income Tax
No, its not.
The EIC is a means-tested social welfare program that has a benefit curve inconsistent with a negative income tax (particularly, it has ranges where more qualifying income increases the beneft, and ranges where it decreases the benefit, whereas the subsidy from a negative income tax is strictly non-increasing with additional income.)