Available quantum computer allows to simulate quantum problems that are not accessible to classical computation. In this talk I will focus on the subset of these problems that relate to quantum transport in one or pseudo-one dimensional systems. I will show that available quantum gates allow extremely accurate simulations and produce expected results for 1D non-interacting chain. I will show that the problems natural for quantum computer that involve discrete time evolution are not less interesting than usual problems with continuous time. I will also argue that quantum computer will allow to resolve the puzzle of quantum diffusion in low dimensional systems in near future.