  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.
