Quantum computation of energy level degeneracy and thermodynamical properties of spin systems

We propose a hybrid quantum-classical method for reconstructing energy-level degeneracies and thermodynamic properties of spin systems. A single ancilla qubit is used to measure the partition function at imaginary inverse temperatures. For spectra lying on a known equally spaced energy grid, the inverse discrete Fourier transform allows exact reconstruction of degeneracies in the absence of noise, without spectral leakage. The quantum circuits are optimized using commuting interactions and Eulerian ordering. We demonstrate the method for frustrated Ising antiferromagnets on periodic Kagome graphs with up to 36 spins, using the ibm_kingston quantum processor. Despite substantial circuit depth and hardware noise, the reconstructed spectra retain their dominant features, and the calculated heat capacities reproduce the main temperature dependence of the exact results. Keywords: partition function, imaginary temperature, Ising model, heat capacity, ancilla qubit, quantum computing.