  General quantum computation consists of unitary operations and also
measurements. It is well known that intermediate quantum measurements can be
deferred to the end of the computation, resulting in an equivalent purely
unitary computation. While time efficient, this transformation blows up the
space to linear in the running time, which could be super-polynomial for
low-space algorithms. Fefferman and Remscrim (STOC'21) and Girish, Raz and Zhan
(ICALP'21) show different transformations which are space efficient, but blow
up the running time by a factor that is exponential in the space. This leaves
the case of algorithms with small-but-super-logarithmic space as incurring a
large blowup in either time or space complexity. We show that such a blowup is
likely inherent, demonstrating that any "black-box" transformation which
removes intermediate measurements must significantly blow up either space or
time.
