  We introduce a novel hybrid quantum-classical algorithm for the near-term
computation of expectation values in quantum systems at finite temperatures.
This is based on two stages: on the first one, a mixed state approximating a
fiducial truncated density matrix is prepared through Variational Quantum
Eigensolving (VQE) techniques; this is then followed by a reweighting stage
where the expectation values for observables of interest are computed. These
two stages can then be iterated again with different hyperparameters to achieve
arbitrary accuracy. Resource and time scalability of the algorithm is discussed
with a near-term perspective.
