Fig. 7: Different correlation functions on hardware.
Results of measuring the real part of the correlation function (a)\({C}_{1,1}^{zz}(t)\), (b)\({C}_{1,2}^{zz}(t)\), (c)\({C}_{1,3}^{zz}(t)\), and (d)\({C}_{0,3}^{zz}(t)\) against Jt for the approximation of the ρ4 Gibbs state are presented. The Hamiltonian employed is the XY model at the inverse temperature β = 0.8. Results were obtained using ibm_algiers, with the qubits' initial layout of [2,1,4,7] for the direct measurements, along with setting t = 5, the number of time steps = 51, dt ≈ 0.1, and the number of shots = 4000. The analytical result of the full ρ4 Gibbs state (gray) is plotted with the hardware simulation result of each order of the approximation against time t. The first (blue), second (green), and third (pink) order hardware results are all plotted. An increase in accuracy is observed with each order of the approximation.
