Unraveling Reverse Annealing: A Study of D-Wave Quantum Annealers

TL;DR

This work investigates reverse annealing on D-Wave quantum annealers, examining how $t_{end}$ and reversal distance $s_r$ shape solution sampling for problems up to 1000 qubits. It combines experimental data with theoretical models, using $H(t)/ bar=rac{ A(s)}{h} H_D+rac{ B(s)}{h} H_P$ and a suite of dissipative frameworks (Lindblad/Bloch and Markovian) to separate quantum from classical contributions. The key finding is that, for sufficiently long total annealing times, the observed state probabilities converge toward thermal equilibrium distributions $p_i^{equil}$ with an effective temperature $T$, suggesting thermalization dominates reverse-annealing dynamics rather than coherent quantum evolution; a simple Markovian model can reproduce many results, indicating practical guidance for problem encoding on D-Wave devices. The study also demonstrates how energy gaps, reversal distance, and problem degeneracy influence equilibration rates, providing a basis for optimizing reverse-annealing protocols and motivating comparisons with forward/fast-annealing modes in future work.

Abstract

D-Wave quantum annealers offer reverse annealing as a feature allowing them to refine solutions to optimization problems. This paper investigates the influence of key parameters, such as annealing times and reversal distance, on the behavior of reverse annealing by studying models containing up to 1000 qubits. Through the analysis of theoretical models and experimental data, we explore the interplay between quantum and classical processes. Our findings provide a deeper understanding that can better equip users to fully harness the potential of the D-Wave annealers

Figures (10)

• Figure 1: (Color online) (a),(b) WTS data and (c),(d) ATS data for the 1-spin problem with $h_1=0.1$ and $s_r=0.7$ obtained from the D-Wave annealer with (a),(c) $\ket{\uparrow}$ and (b),(d) $\ket{\downarrow}$ as initial states.
• Figure 2: (Color online) WTS data for the 2-spin problem instance (a) 2S1, (b) 2S2, and (c) 2S3 obtained from the D-Wave annealer with $s_r=0.7$.
• Figure 3: (Color online) Comparison of Bloch equations simulation results with those from the D-Wave annealer for (a) WTS and (b) ATS for the 1-spin problem with $h_1=0.1$ and $s_r=0.7$. For (a) $T_1 = 41.67~\mu s$, $T_2 = 41.67~\mu s$, and $M_0 =-0.66$ while for (b) $T_1=909.09~\mu s$, $T_2=909.09~\mu s$, and $M_0=-0.66$. To emphasize that each data point from the simulations is obtained from an independent run we show each simulation data point as a marker. For improved legibility, in the subsequent figures, data points from our simulations are represented by lines through these points instead of by markers.
• Figure 4: (Color online) Comparison of the WTS data from Bloch equation simulations (lines) for the 1-spin problem with $s_r=0.7$ and (a) $h_1=0$ and (b) $h_1=0.001$ with the D-Wave data (markers) for the same with $h_1=0$. For both plots $T_1=25~\mu s$, $T_2=25~\mu s$, and $M_0=0$.
• Figure 5: (Color online) Comparison of the ATS data from D-Wave (markers) with that from Lindblad master equation simulation (lines) for 2-spin instances with $s_r=0.7$ (a) 2S1, (b) 2S2, and (c) 2S3, with dissipation rates (a) $\gamma_1=\gamma_3=\gamma_4=\gamma_6=1.5$ Hz, $\gamma_2=0$, $\gamma_5=\gamma_7=0.6582$ Hz, (b) $\gamma_1=\gamma_3=\gamma_4=\gamma_6=1.0$ Hz, $\gamma_2=0$, $\gamma_5=\gamma_7=0.9837$ Hz, (c) $\gamma_1=\gamma_3=\gamma_4=\gamma_6=0.5$ Hz, $\gamma_2=0$, $\gamma_5=\gamma_7=1.1395$ Hz.