We assess the resources needed to identify a reversible quantum gate among a
finite set of alternatives, including in our analysis both deterministic and
probabilistic strategies. Among the probabilistic strategies we consider
unambiguous gate discrimination, where errors are not tolerated but
inconclusive outcomes are allowed, and we prove that parallel strategies are
sufficient to unambiguously identify the unknown gate with minimum number of
queries. This result is used to provide upper and lower bounds on the query
complexity and on the minimum ancilla dimension. In addition, we introduce the
notion of generalized t-designs, which includes unitary t-designs and group
representations as special cases. For gates forming a generalized t-design we
give an explicit expression for the maximum probability of correct gate
identification and we prove that there is no gap between the performances of
deterministic strategies an those of probabilistic strategies. Hence,
evaluating of the query complexity of perfect deterministic discrimination is
reduced to the easier problem of evaluating the query complexity of unambiguous
discrimination. Finally, we consider discrimination strategies where the use of
ancillas is forbidden, providing upper bounds on the number of additional
queries needed to make up for the lack of entanglement with the ancillas.Comment: 24 + 8 pages, published versio