  A t-design for quantum states is a finite set of quantum states with the
property of simulating the Haar-measure on quantum states, w.r.t. any test that
uses at most t copies of a state. We give efficient constructions for
approximate quantum t-designs for arbitrary t. We then show that an approximate
4-design provides a derandomization of the state-distinction problem considered
by Sen (quant-ph/0512085), which is relevant to solving certain instances of
the hidden subgroup problem.
