  We provide an alternative proof of \class{QIP}=\class{PSPACE} to the recent
breakthrough result. Unlike solving some semidefinite programs that captures
the computational power of quantum interactive proofs, our method starts with
one \class{QIP}-Complete problem which computes the diamond norm between two
admissible quantum channels. The key observation is that we can convert the
computation of the diamond norm into the computation of some equilibrium value.
The later problem, different from the former semidefinite programs, is of
better form, easier to solve and could be interesting for its own sake. The
multiplicative weight update method is also applied to solve the equilibrium
value problem, however, in a relatively simpler way than the one in the
original proof. As a direct byproduct, we also provide a NC algorithm to
compute the diamond norm of a class of quantum channels. Furthermore, we
provide a generalized form of equilibrium value problems that can be solved in
the same way as well as comparisons to semidefinite programs.
