  We present a new parallel numerical method for solving the non-stationary
Schr\"odinger equation with linear nonlocal condition and time-dependent
potential which does not commute with the stationary part of the Hamiltonian.
The given problem is discretized in-time using a polynomial-based collocation
scheme. We establish the conditions on the existence of solution to the
discretized problem, estimate the accuracy of the discretized solution and
propose the method how this solution can be approximately found in an efficient
parallel manner.
