Post-selection, the power of discarding all runs of a computation in which an undesirable event occurs, is an influential concept introduced to the field of quantum complexity theory by Aaronson (Proceedings of the Royal Society A, 2005). In the present paper, we initiate the study of post-selection for space-bounded quantum complexity classes. Our main result shows the identity $\sf PostBQL=PL$, i.e., the class of problems that can be solved by a bounded-error (polynomial-time) logarithmic-space quantum algorithm with post-selection ($\sf PostBQL$) is equal to the class of problems that can be solved by unbounded-error logarithmic-space classical algorithms ($\sf PL$). This result gives a space-bounded version of the well-known result $\sf PostBQP=PP$ proved by Aaronson for polynomial-time quantum computation. As a by-product, we also show that $\sf PL$ coincides with the class of problems that can be solved by bounded-error logarithmic-space quantum algorithms that have no time bound.

翻译：Aaronson(皇家学会A,2005年)在量子复杂理论领域引入了一个有影响力的概念,Aaronson(皇家学会A号,2005年)对量子复杂理论领域提出了放弃所有运行的计算结果的力量。在本文件中,我们开始研究空间限制量子复杂等级的后选问题。我们的主要结果显示身份 $\ sf PostBQL=PL$,即Aaronson证明通过受约束的(Polynomiaal-time)对数值算法($\sf PostBQL$)可以解决的问题类别。我们还表明,美元/ PL$与不受约束的对数空间经典算法无法解决的时空问题类别相等。