Fig. 5: Bubble interactions.
From: Stirring the false vacuum via interacting quantized bubbles on a 5,564-qubit quantum annealer
a, Time series measurements of the bubble density at the 1-bubble resonance (hz = –2J and hx = 0.002). During the initial hz(t) modulation, the profile of which is shown by the black curve on the right axis, the 1-bubble density (colour bar) governs the dynamics. After about ~0.75 μs (dashed line), thermalization effects take over by transforming 1-bubbles into 3- and 5-bubbles. b, Measurement of the emergent blockade QB and magnetization M (right axis) at hx = 0.002 and t = 0.38 μs, plotted as a function of hz magnitude. The blockade condition is violated (deviates from 0) only at hz values significantly off the 1-bubble resonance (hz ≤ – 3.5), accompanied by large changes in M. Near resonance (hz ≈ – 2), even though large changes in M occur, the blockade condition is respected. c,d, Dynamics at the resonance hz = –J with fixed hx = 0.0203 (c) and hx = 0.002 (d). MPS simulation with 100 qubits in c captures some of the key aspects of the data obtained on the quantum annealer in d. Panel c shows the sudden change in the number of 2-bubbles when hz(t) is exactly at the resonance point (dashed horizontal line). The inset magnifies the low-density regime, where only 1- and 3-bubbles can be seen. The increase in 1- and 3-bubbles is probably due to 2-bubbles interacting. The quantum simulation using hx = 0.002 in d shows good agreement with the theoretical prediction in c. For all the measured data, the error bars come from counting errors on the annealer and are smaller than the symbol size. e, MPS simulation of the dynamics after an instantaneous quench from a product state shown at the bottom, containing two large bubbles (n1 = 23 and n2 = 24 spins) next to each other in a system with a total of 50 spins. The system undergoes coherent evolution with fixed hz = –1 and hx = 0.02, and the colour bar shows the ‘bubble interface density’, \(\langle {\hat{P}}_{j-1}^{\downarrow }{\hat{P}}_{j}^{\uparrow }{\hat{P}}_{j+1}^{\downarrow }\rangle\), on a log scale and for all sites j. The moving front corresponds to the two bubbles exchanging ↓ spins and changing their sizes. The final state at the end of the evolution is a quantum superposition, with one of the classical configurations shown at the top.
