The conventional approach for simulating quantum systems is to solve the time-dependent Schrödinger equation of the corresponding system. In practice, this amounts to multiplying the state vector by a sequence of (many) unitary matrices. According to quantum theory, the squares of the amplitudes of the final state of the quantum system yield the probabilities for observing the system in a particular basis state.
In the event-based simulation approach we construct processes that generate events of which the ratio of occurrence agrees with quantum theory. Thus, adopting this method, we don’t use concepts of quantum theory at all: We don’t use wave functions or the Schrödinger equation and do not run into the notorious measurement problem. In our approach, quantum mechanical behavior is the result of a causal, deterministic (or stochastic), event-based process.
More information about this simulation method and its applications can be found on these very old webpages DLM (no longer maintained)