2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/123361A 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.19 pages, v2 two references added, to appear in Complexity'06Quantum Physicstext