Expectations from the Liouville-von Neumann Equation Using Chebyshev Expansion

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.