  In this paper, we systematically study property testing of unitary operators.
We first introduce a distance measure that reflects the average difference
between unitary operators. Then we show that, with respect to this distance
measure, the orthogonal group, quantum juntas (i.e. unitary operators that only
nontrivially act on a few qubits of the system) and Clifford group can be all
efficiently tested. In fact, their testing algorithms have query complexities
independent of the system's size and have only one-sided error. Then we give an
algorithm that tests any finite subset of the unitary group, and demonstrate an
application of this algorithm to the permutation group. This algorithm also has
one-sided error and polynomial query complexity, but it is unknown whether it
can be efficiently implemented in general.
