You can probably find a few condensed matter groups that are doing computational simulations, but I think full quantum mechanical simulations on that scale are

You can probably find a few condensed matter groups that are doing computational simulations, but I think full quantum mechanical simulations on that scale are computationally intractable so they'll have to use approximations of some sort. This is why quantum computers are predicted to exceed the computational power of classical computers. Besides it's been fairly recent that simulations for classical thermodynamics with a decent number of particles became somewhat feasible. And even then it often uses lots of approximations as well as statistical tricks to get decent results for sizeable systems. For quantum mechanics quite a few tricks to explore the state-space stop working because the state-space is unimaginably huge, so I'm not even sure how to begin to do similar simulations, but I reckon they'll be disastrously slow for all but the simplest of systems. The level of detail you need for a simulation that allows you to see cooper pairs come into existence is downright insane, you might be better of trying to predict next years weather.