Cheers
The most promising variety of quantum computation currently available is D-Wave's quantum annealing approach, which isn't a "standard" quantum computer, but unlike its competitors it does actually exist in a production variety and seems to have some big customers.
From what I can tell, it could be useful for machine learning, which could then in turn (practicalities and expenses aside) theoretically be used for game AI. It's also useful for physics simulation, apparently, with people simulating quantum systems like spinglasses on their hardware. If scaled up, it could be something that gets used for interesting game physics.
Problem is, right now it's somewhat difficult and expensive to get access to these systems, so I don't think you'll see them in gaming for a long time.
Instead, you're more likely to experience quantum computing as the game itself - like http://play.quantumgame.io/
Maybe someone will take this concept further and make a quantum variant of Shenzhen I/O or something like that.