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arXiv:2608.04564

Quantum annealers as programmable thermal machines

Jakub Pawłowski, Tomasz Śmierzchalski, Fengping Jin, Bartłomiej Gardas, Sebastian Deffner, Zakaria Mzaouali

quant-phSubmitted Aug 5, 2026• Announced Aug 6, 2026• 0 citations
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Abstract

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.

Comments
21 pages, 9 figures

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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.
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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.
Quantum annealing targets low-energy solutions of Ising/QUBO problems, but reliable assessment requires more than best-energy comparisons. This dissertation develops a benchmarking framework for D-Wave quantum annealers that combines strong classical baselines, sampling and diversity metrics, and thermodynamic cost. Its first contribution, SpinGlassPEPS...jl, is a topology-aware tensor-network heuristic for optimization and sampling on Pegasus/Zephyr-like graphs. It maps Ising instances to local Potts clusters, represents the partition function with PEPS, and performs branch-and-bound search in probability space. Benchmarks show that it is a physically interpretable reference solver, though approximate contractions limit its competitiveness on the largest instances. The second contribution treats quantum annealers as effective thermal machines, relating success probability and solution quality to dissipation, entropy production, and effective temperature. Carefully placed pauses can improve performance while reducing thermodynamic cost, although longitudinal fields may become harmful in paused schedules. The thesis also introduces reinforcement-learning post-processing to improve returned samples and exact small-system simulations to probe annealing dynamics. Overall, it argues for quantum-annealing benchmarks that jointly measure algorithmic performance and physical expenditure.
Quantum annealers are emerging as programmable, dynamical experimental platforms for probing strongly correlated spin systems. Yet key thermal assumptions, chiefly a Gibbs-distributed output ensemble, remain unverified in the large-scale regime. Here, we experimentally and quantitatively assess Gibbs sampling fidelity across system sizes spanning over three orders of magnitude. We explore a wide parameter space of coupling strengths, system sizes, annealing times, and D-wave hardware architectures. We find that the naively assumed scaling law for the effective temperature requires a non-negligible, coupling-independent offset that is robust across machines and parameter regimes, quantifying residual non-thermal effects that still conform to an effective Gibbs description. These non-idealities are further reflected in a systematic discrepancy between the physical temperature inferred from the sampled ensemble and the nominal cryogenic temperature of the device. Our results systematically assess the viability of quantum annealers as experimental platforms for probing classical thermodynamics, correct previous assumptions, and provide a physically grounded thermometry framework to benchmark these machines for future thermodynamic experiments.
Reverse annealing is widely used as a heuristic sampler on programmable quantum annealers, but it is often unclear whether the readout has erased its initialization memory or whether the resulting samples represent any calibrated target distribution. We introduce a subsystem-level validation protocol that pairs a memory order parameter M\mathcal{M}M with the total-variation distance DTVD_{\mathrm{TV}}DTV​ between the measured subsystem readout and a fixed, independently calibrated conditional-Boltzmann reference, and apply it on two D-Wave QPU generations. The protocol delivers three things: a diagnostic that separates relaxed, memory-retaining and "wrong-basin" readouts; the isolation of relaxed-but-non-thermal trapping, in which a readout passes the initial-state-independence test while concentrating on the wrong basin; and an engineering control showing that SDK auto-scale, embedding choice and environment preparation shift apparent thresholds, so calibration metadata must be logged to interpret them. Relaxed ferromagnetic readouts are near-deterministic, so the small distances seen there are a consistency check rather than a thermometric measurement; the diagnostic earns its value in the opposite regime. Across 494 conditions on one processor, 113 pass the memory criterion and 110 of those agree with the reference at DTV<0.05D_{\mathrm{TV}}<0.05DTV​<0.05, while a wrong-basin instance, reproduced at two Hamiltonian scales, passes the memory test yet reaches DTV>0.94D_{\mathrm{TV}}>0.94DTV​>0.94; a 60-condition replication confirms that the diagnostic transfers to a second processor. We provide the protocol as a transferable, reproducible validation workflow for annealer-as-sampler applications.