Fig. 4. Numerical phase diagram and experimental detection of the phase transition.

a, The numerical δ−V phase diagram obtained by examining the central subharmonic peak height for the edge spins in the Fourier spectrum, averaged over 50,000 disorder instances. The dashed line corresponds to the maximal height variances for varying V with each fixed δ point, which gives a rough estimation of the phase boundary. Here, the parameters are chosen as L = 8, J = Δ_j = 1 and h = Δ_h = Δ_V = 0. b, Experimental result of the subharmonic peak height as a function of δ with fixed h = V = Δ_h = Δ_V = 0 and J = Δ_j = 1, averaged over 50 disorder instances uniformly sampled from the interval [J − Δ_J, J + Δ_J] for L = 8 qubits, with the shadow outlining the standard deviation. Inset: the standard deviation of the central peak height as a function of δ. The purple vertical dashed line at δ = 0.34 indicates the numerically determined phase boundary from a. The dashed lines in grey show numerical simulations with experimental noises taken into account.