Fig. 3: Scaling laws for bubble dynamics.
From: Stirring the false vacuum via interacting quantized bubbles on a 5,564-qubit quantum annealer
a, 2-bubble density at hx = 0.002 as a function of time at various hz magnitudes (colour bar). The inset shows the collapse of different curves when time is rescaled by \({h}_{z}^{2}\) in accordance with the Landau–Zener theory35. b,c, Magnetization at hz = –J resonance as a function of rescaled time \({h}_{x}^{2}t\), for different values of hx indicated on the colour bar. Both the measured magnetization curves in b and the three-spin Bloch–Redfield numerical simulations in c follow the same \({h}_{x}^{2}\) scaling law, suggesting that the effective Hamiltonian governing the dynamics is proportional to \({h}_{x}^{2}\). The inset in b shows the raw data obtained on the quantum annealer without rescaling. The unscaled results of the numerical simulations are shown in the inset of c, where the black curves show the magnetization in the effective model describing the hz = –J resonance (Methods). The error bars in a and b come from counting errors on the annealer and are smaller than the size of the symbols.
