We show that quantum algorithms of time T and space S \ge \log T with intermediate measurements can be simulated by quantum algorithms of time T\cdot \mathrm{poly}(S) and space O(S\cdot \log T) without intermediate measurements. The best simulations prior to this work required either \Omega(T) space (by the deferred measurement ... more >>>

We introduce two models of space-bounded quantum interactive proof systems, \mathbf{QIPL} and \mathbf{QIP_\mathrm{U}L}. The \mathbf{QIP_\mathrm{U}L} model, a space-bounded variant of quantum interactive proofs (\mathbf{QIP}) introduced by Watrous (CC 2003) and Kitaev and Watrous (STOC 2000), restricts verifier actions to unitary circuits. In contrast, \mathbf{QIPL} allows logarithmically many intermediate measurements per ... more >>>