证明后选择的力量
Proving the power of postselection
摘要：
这是一个被广泛认为，但未经证实的猜想，后选择的能力增加了概率和量子多项式时间计算机的语言识别能力。也不知道具有后选择的多项式时间量子机是否比具有相同资源限制的概率量子机更强大。我们通过对计算机所使用的资源施加额外的约束来解决这些问题，并且能够首次证明后选择确实增加了经典计算机和量子计算机的计算能力，并且在一定范围内的同时时间和空间界限下，量子在这种情况下确实优于概率。我们还着眼于后选择版本的空间有界类，以及相应的无错和片面的错误识别，并提供经典的刻画。结果表明，如果随机机具有后选择能力，则$\mathsf{NL}$将等于$\mathsf{RL}$.
英文摘要：
It is a widely believed, though unproven, conjecture that the capability of postselection increases the language recognition power of both probabilistic and quantum polynomial-time computers. It is also unknown whether polynomial-time quantum machines with postselection are more powerful than their probabilistic counterparts with the same resource restrictions. We approach these problems by imposing additional constraints on the resources to be used by the computer, and are able to prove for the first time that postselection does augment the computational power of both classical and quantum computers, and that quantum does outperform probabilistic in this context, under simultaneous time and space bounds in a certain range. We also look at postselected versions of space-bounded classes, as well as those corresponding to error-free and one-sided error recognition, and provide classical characterizations. It is shown that $\mathsf{NL}$ would equal $\mathsf{RL}$ if the randomized machines had the postselection capability.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
