  A foundational result in the theory of quantum computation known as the
"principle of safe storage" shows that it is always possible to take a quantum
circuit and produce an equivalent circuit that makes all measurements at the
end of the computation. While this procedure is time efficient, meaning that it
does not introduce a large overhead in the number of gates, it uses extra
ancillary qubits and so is not generally space efficient. It is quite natural
to ask whether it is possible to defer measurements to the end of a quantum
computation without increasing the number of ancillary qubits.
  We give an affirmative answer to this question by exhibiting a procedure to
eliminate all intermediate measurements that is simultaneously space-efficient
and time-efficient. A key component of our approach, which may be of
independent interest, involves showing that the well-conditioned versions of
many standard linear-algebraic problems may be solved by a quantum computer in
less space than seems possible by a classical computer.
