平衡值法证明QIP = PSPACE
Equilibrium Value Method for the Proof of QIP=PSPACE
摘要：
对最近的突破性结果给出了\class{QIP} = \class{PSPACE}的另一种证明.不像解决一些半定的程序，捕获量子交互式证明的计算能力，我们的方法开始于一个\class{QIP} -完全问题，计算两个容许的量子信道之间的钻石范数。关键的观察是，我们可以将钻石范数的计算转换为某个均衡值的计算。后者的问题，不同于以前的半定规划，是更好的形式，更容易解决，可能是有趣的，因为它本身的缘故。乘性权值更新方法也适用于解决平衡值问题，但在一个相对简单的方式比原来的证明。作为一个直接的副产品，我们还提供了一个NC算法来计算一类量子信道的钻石范数。此外，我们提供了一个广义形式的平衡值问题，可以解决以同样的方式，以及比较半定规划。
英文摘要：
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.
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