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 >>>