Fig. 4: Experimental diagonalization of many-body Hamiltonians.

a The energy per site of Heisenberg model for particle numbers k = 1, 3, and 5 in system sizes of N = 56, 44, and 42, respectively. The error bars indicate standard deviations estimated by bootstrapping. The dashed curves indicate the energies from noiseless classical simulations, and solid black lines show the exact lowest energy in the given k-particle subspace. b–d Qubit layout graphs. The green and red circles indicate the control and initial locations of particles, respectively. e–g Energy curves for individual particle numbers k = 1, 3, and 5. h–j Error matrices \(\Delta \tilde{H}/N :=| {\tilde{H}}_{\exp }-{\tilde{H}}_{{\rm{num}}}| /N\) and \(\Delta \tilde{S} :=| {\tilde{S}}_{\exp }-{\tilde{S}}_{{\rm{num}}}|\), where the subscripts “exp" and “num" denote data from experiments and numerical calculations, respectively.