Anti-matter is produced at CERN for study https://home.cern/topics/antimatter.

The problem is not production of it but the economy of producing it. It's still very costly to produce and then to build and engine around it which uses the energy efficiently is still at least 10-15 years. But do believe that the time to start actively looking into it is NOW.

Is it stable enough to survive a space launch?

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.

As a practical matter most of the byproducts of antimatter annihilation aren't amenable to being directed out the rear of a spacecraft by a nozzle, magnetic or otherwise. So the maximum theoretical efficiency is possibly better with advanced fusion drives than with antimatter.

When discussing antimatter for propulsion, it might be worth checking out Robert L Forward. I saw the expression that he took the "giggle factor" out of the subject. :-)

I found this overview, discussing a bit about the antimatter research:

http://www.enthea.org/docs/Forward-Emerging-Technologies-Fut...