We initiate the study of the relationship between two complexity classes, BQP
(Bounded-Error Quantum Polynomial-Time) and PPAD (Polynomial Parity Argument,
Directed). We first give a conjecture that PPAD is contained in BQP, and show
a necessary and sufficient condition for the conjecture to hold. Then we prove
that the conjecture is not true under the oracle model. In the end, we raise
some interesting open problems/future directions.