Calculation of partition function of Ising model on quantum computer

We study the partition function of the Ising model on a graph with the help of quantum computing. The Boltzmann factor is modeled on a quantum computer as a trace of some evolution operator with effective Hamiltonian over ancilla spins (qubits) corresponding to graph links. We propose two methods for this which are based on effective Hamiltonian with three-spin interaction and on two-spin interaction. The limit of small temperatures allows us to find the ground state of the system that is related to the discrete combinatorial optimization problem. The partition function of the Ising model for two-spin clusters is calculated on IBM's quantum computer. The possibility of finding ground state is also demonstrated for two-spin clusters.