Fig. 3: Quantum simulation of single- and multi-mode measurements.
From: Quantum simulation of thermodynamics in an integrated quantum photonic processor
a Hopping Hamiltonian (superfluid): In panel I, the time evolution of photon-number probability distribution in spatial output mode 1 is plotted. The black points (squares) show the theoretical prediction for indistinguishable (distinguishable) particles, while colored points correspond to experimental data. Panels II–IV show the observed output distributions. These rows correspond to the output distributions of the hopping Hamiltonian (panel II), the first certification measurement U−1 (panel III), and the second certification measurement UFU−1 (panel IV). Theoretical predictions (Th) are represented by bars, and the experimental results (Exp) are represented by circles. The green-colored data corresponds with outcomes that benefit the certification protocol, whereas the red data is forbidden, i.e., ideally, should not occur. b Long-range Hamiltonian (Haar random): In panel I, the time evolution of photon-number probability distribution in spatial output mode 1 for 20 different random Hamiltonians is plotted. The black points (squares) show the theoretical prediction for indistinguishable (distinguishable) particles, while colored points correspond to experimental data. Panels II–IV show the observed output distributions for the first long-range Hamiltonian. These rows correspond to the output distributions of the first long-range Hamiltonian (panel II), the first certification measurement U−1 (panel III), and the second certification measurement UFU−1 (panel IV). Theoretical predictions (Th) are represented by bars, and the experimental results (Exp) are represented by circles. The green-colored data corresponds with outcomes that benefit the certification protocol, whereas the red data is forbidden, i.e., ideally, should not occur.
