We investigate the computational efficiency and thermodynamic cost of the D-Wave quantum annealer under reverse-annealing with and without pausing. Our demonstration on the D-Wave 2000Q annealer shows that the combination of reverse-annealing and pausing leads to improved computational efficiency while minimizing the thermodynamic cost compared to reverse-annealing alone. Moreover, we find that the magnetic field has a positive impact on the performance of the quantum annealer during reverse-annealing but becomes detrimental when pausing is involved. Our results, which are reproducible, provide strategies for optimizing the performance and energy consumption of quantum annealing systems employing reverse-annealing protocols.
We investigate the computational efficiency and thermodynamic cost of the D-Wave quantum annealer under reverse-annealing with and without pausing. Our demonstration on the D-Wave 2000Q annealer shows that the combination of reverse-annealing and pausing leads to improved computational efficiency while minimizing the thermodynamic cost compared to reverse-annealing alone. Moreover, we find that the magnetic field has a positive impact on the performance of the quantum annealer during reverse-annealing but becomes detrimental when pausing is involved. Our results, which are reproducible, provide strategies for optimizing the performance and energy consumption of quantum annealing systems employing reverse-annealing protocols.
Quantum annealing is a promising heuristic for combinatorial optimization, but on current hardware its performance degrades for larger and more complex problems due to noise and small energy gaps. Reverse annealing has been proposed as a refinement strategy, yet it remains unclear when it provides systematic advantages over standard forward annealing or simply increasing annealing time. We find that combining forward and reverse annealing consistently improves solution quality and efficiency across multiple problem classes. The benefits of reverse annealing increase with problem complexity and are strongest in regimes where forward annealing is increasingly limited. Moreover, reverse annealing yields larger efficiency gains than simply extending forward annealing times. We establish these results through a systematic experimental study on a D-Wave Advantage system, benchmarking reverse annealing across Max-Cut, Number Partitioning, and sparse clustering problems while varying reverse distance, pause duration, and annealing time. We identify a narrow optimal regime for reverse annealing parameters linked to the location of freeze-out points and energy-level crossings in the annealing schedule. These findings demonstrate that reverse annealing is most valuable for large, high-complexity optimization problems and is likely to gain importance as quantum annealing hardware scales toward more realistic applications.
In reverse quantum annealing, the initial state is an eigenstate of the final problem Hamiltonian and the transverse field is cycled rather than strictly decreased as in standard (forward) quantum annealing. We present a numerical study of the reverse quantum annealing protocol applied to the p-spin model (p=3), including pausing, in an open-system setting accounting for dephasing in the energy eigenbasis, which results in thermal relaxation. We consider both independent and collective dephasing and demonstrate that in both cases the open-system dynamics substantially enhances the performance of reverse annealing. Namely, including dephasing overcomes the failure of purely closed-system reverse annealing to converge to the ground state of the p-spin model. We demonstrate that pausing further improves the success probability. The collective dephasing model leads to somewhat better performance than independent dephasing. The protocol we consider corresponds closely to the one implemented in the current generation of commercial quantum annealers, and our results help to explain why recent experiments demonstrated enhanced success probabilities under reverse annealing and pausing.
The D-wave processor is a partially controllable open quantum system which exchanges energy with its surrounding environment (in the form of heat) and with the external time dependent control fields (in the form of work). Despite being rarely thought as such, it is a thermodynamic machine. Here we investigate the properties of the D-Wave quantum annealers from a thermodynamical perspective. We performed a number of reverse-annealing experiments on the D-Wave 2000Q via the open access cloud server Leap, with the aim of understanding what type of thermal operation the machine performs, and quantifying the degree of dissipation that accompanies it, as well as the amount of heat and work that it exchanges. The latter is a challenging task in view of the fact that one can experimentally access only the overall energy change occurring in the processor, (which is the sum of heat and work it receives). However, recent results of non-equilibrium thermodynamics(namely, the fluctuation theorem and the thermodynamic uncertainty relations), allow to calculate lower bounds on the average entropy production (which quantifies the degree of dissipation) as well as the average heat and work exchanges. The analysis of the collected experimental data shows that 1) in a reverse annealing process the D-Wave processor works as a thermal accelerator and 2) its evolution involves an increasing amount of dissipation with increasing transverse field.
Programmable quantum annealers are used for optimization, probabilistic sampling, and simulation, but their performance is commonly reported without the energy exchanged during computation. Here we characterize the D-Wave quantum annealer as a closed thermodynamic cycle. From initial and final Ising energies and an effective temperature fitted to the output distribution, we obtain lower bounds on entropy production, environment energy exchange, work, and power. By varying the prepared distribution and the reverse annealing turning point, we map heater-, accelerator-, refrigerator-, and engine-compatible regimes in one dimensional chains and higher connectivity instances, and apply the same analysis to Advantage and Advantage2 hardware. For an encoded optimization problem, the measured processor energy change states whether final candidates improve or worsen the programmed objective on average. For sampling, the fitted temperature provides an operational measure of how strongly probability is concentrated among low energy configurations. The thermodynamic mode therefore adds information absent from solution quality or runtime alone: it distinguishes driven refinement, net heating, and heat pumping while quantifying their energetic consequences. This framework connects quantum optimization, probabilistic computing, statistical physics simulation, hardware diagnostics, and energy-aware assessment without assuming that a thermodynamic label alone determines computational performance.
Abstract The D-wave processor is a partially controllable open quantum system that exchanges energy with its surrounding environment (in the form of heat) and with the external time dependent control fields (in the form of work). Despite being rarely thought as such, it is a thermodynamic machine. Here we investigate the properties of the D-Wave quantum annealers from a thermodynamical perspective. We performed a number of reverse-annealing experiments on the D-Wave 2000Q via the open access cloud server Leap, with the aim of understanding what type of thermal operation the machine performs, and quantifying the degree of dissipation that accompanies it, as well as the amount of heat and work that it exchanges. The latter is a challenging task in view of the fact that one can experimentally access only the overall energy change occurring in the processor, (which is the sum of heat and work it receives). However, recent results of non-equilibrium thermodynamics (namely, the fluctuation theorem and the thermodynamic uncertainty relations), allow to calculate lower bounds on the average entropy production (which quantifies the degree of dissipation) as well as the average heat and work exchanges. The analysis of the collected experimental data shows that (1) in a reverse annealing process the D-Wave processor works as a thermal accelerator and (2) its evolution involves an increasing amount of dissipation with increasing transverse field.
Recent research has shown that alternative annealing schedules provide the means for improving performance in modern quantum annealing devices. One such type of schedule is forward annealing with a pause, in which there is a period of time when system evolution is paused. While the results from using this type of schedule have been promising, effectively using a pause is not a trivial task. One challenge associated with introducing a pause into the schedule is determining the point in the anneal at which the pause will start. Additionally, tuning the schedule in real-time requires a significant amount of time. A second challenge is that while a pause may increase the number of correct solutions returned from the annealer, the time-to-solution, a standard metric for measuring performance in quantum annealing, will not necessarily be improved. We propose a method for constructing annealing schedules containing a pause that avoids the costly process of determining the optimal pause location in an online manner. We also evaluate our method on the subset sum problem, a problem of practical significance, and show that our method is able to achieve a 70% reduction in time-to-solution from a standard schedule containing no pause.