don't think so. I am guessing you would need really strong magnetic fields to contain the anti-matter.

Magnetic fields aren't the only issue here.

You won't be able to store large amounts of it since quantum tunneling will become a statistical problem.

Could you explain? How would quantum tunneling of antimatter be a problem?

The probability of quantum tunneling is exponential so adding a little more separation or reducing the energy can change the probability from 10^-1 to 10^-100.