Testing quantum expanders is co-QMA-complete
  A quantum expander is a unital quantum channel that is rapidly mixing, has only a few Kraus operators, and can be implemented efficiently on a quantum computer. We consider the problem of estimating the mixing time (i.e., the spectral gap) of a quantum expander. We show that this problem is co-QMA-complete. This has applications to testing randomized constructions of quantum expanders, and studying thermalization of open quantum systems. 
Adam D. Bookatz and Stephen P. Jordan and Yi-Kai Liu and Pawel Wocjan
quant-ph