Continuing the discussion from Quantum Life in a Computer? Really?:
However, this excellent article on quantum verification was just published, highlighting the work of a graduate student that solved a problem no one knew if it could be solvable. The task: how do we set up a problem so a classical (non-quantum) user can figure out if a quantum computer is really doing a quantum calculation. This is a really important and open problem, until just recently. She managed to solve this during her PhD. Very impressive.