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

Equilibrium Value Method for the Proof of QIP=PSPACE