  We investigate quantum inspired algorithms to compute physical observables of
quantum many-body systems at finite energies. They are based on the quantum
algorithms proposed in [Lu et al. PRX Quantum 2, 020321 (2021)], which use the
quantum simulation of the dynamics of such systems, as well as classical
filtering and sampling techniques. Here, we replace the quantum simulation by
standard classical methods based on matrix product states and operators. As a
result, we can address significantly larger systems than those reachable by
exact diagonalization or by other algorithms. We demonstrate the performance
with spin chains up to 80 sites.
