The two main branches of research into realizing a quantum computer are photonics and nuclear magnetic resonance.  Both of which have their issues, but there's been some interesting research in converting entangled states of one "medium" into another, if you will.  The main issue is the fact that we will never have a truly closed quantum system.  Between external potentials and pre-existing external entanglement, you introduce bias towards certain states, which ruins the computation.  Scaling up the qubit registers and circuits only amplifies this bias further.  Error correcting circuits can help with this, but the circuit complexity then increases accordingly (I believe this is a n*log(n) relation IIRC).