This paper presents the first quantum computational 
characterization of the Graph Non-Isomorphism problem (GNI).
We show that GNI is in a quantum non-deterministic 
polynomial-time class,
i.e., quantum Merlin-Arthur game class (QMA)
or quantum probabilistic NP (BQNP).
In other words, given two graphs (G_0,G_1) in GNI,
(G_0,G_1) has a polynomial-size quantum certificate
with which (G_0,G_1) in GNI can be convinced by a polynomial-time
(probabilistic) quantum Turing machine.