  We consider a natural dimension reduction technique for the Liouville-von
Neumann equation for a mixed quantum system based on evaluation of a trace
formula combined with a direct expansion in modified Chebyshev polynomials.
This reduction is highly efficient and does not destroy any information. We
demonstrate the practical application of the scheme with a model problem and
compare with popular alternatives. This method can be applied to autonomous
quantum problems where the desired outcome of quantum simulation is the
expectation of an observable.
