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Quantum algorithms are well-suited to calculate estimates of the energyspectra for spin lattice systems. These algorithms are based on the efficientcalculation of the discrete Fourier components of the density of states. Theefficiency of these algorithms in calculating the free energy per spin ofgeneral spin lattices to bounded error is examined. We find that the number ofFourier components required to bound the error in the free energy due to thebroadening of the density of states scales polynomially with the number ofspins in the lattice. However, the precision with which the Fourier componentsmust be calculated is found to be an exponential function of the system size.Comment: 9 pages, 4 figures; corrected typographical and minor mathematical  error

Efficiency of free-energy calculations of spin lattices by spectral quantum algorithms