Fig. 3: Excitation dynamics and the emergent U(1) × U(1) symmetry.

a–c, Measured site-resolved dynamics of normalized expectation value \(\overline{\langle {K}_{i}\rangle }\) for the homogeneous (J_o = J_e = π/5) (a), the dimerized but resonant (J_o = 2J_e = 2π/5) (b) and the dimerized and off-resonant (J_o = 3.17J_e = 3.17π/5) (c) cases. For \(\overline{\langle {K}_{i}\rangle }\) at odd (even) sites, colour bars are chosen to be red (blue) for a better visualization of the excitation dynamics. d–f, Measured time dynamics of the total excitation number n, and of the excitation number at even (n_e) and odd (n_o) sites, which are extracted from a to c. In the homogeneous case (d), the values of n_e and n_o gradually converge, yet their sum remains approximately constant, reflecting the U(1) symmetry on the total excitation number n in the bulk. In the dimerized but resonant case (e), the exchange of excitations between two Kitaev chains, which happens near the left edge, can be observed through the decrease of n_o and increase of n_e. By contrast, in the dimerized and off-resonant case (f), n_e and n_o are conserved independently, indicating an emergent U(1) × U(1) symmetry. The grey dashed lines represent the initial values of n_o = 6, n_e = 10, n = 16 and n_e + 2n_o = 22 in e. Error bars represent the standard deviation over five rounds of measurements, with each taking 20,000 shots.