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 >>>