On a mixed-frustration 12-qubit Ising instance run on two D-Wave generations, Advantage2 Zephyr and Advantage_system6.4 Pegasus, the late-time subsystem autocorrelation under cycled reverse annealing sits strictly between two equilibrium reference processes at the device-calibrated effective temperature: localized parallel tempering, and delocalized equilibrated path-integral simulated quantum annealing at a fixed Advantage2 pause-point transverse-field scale. The bracket holds on all three tested schedules and at both hardware calibrations. We obtain this result through two ingredients: a cycled reverse-anneal protocol (reinitialize_state=False, 50 cycles per submission) used as a Markov-chain probe of the device's pause-point dynamics, and a parallel-tempering falsification framework with bias-corrected and accelerated bootstrap 95% confidence intervals. Of eighteen tested (instance, schedule) combinations on Advantage2, three are PT-unmatched and correspond to two distinct Ising instances; an independent native-graph control with no minor embedding on a third mixed-frustration instance reproduces the same direction of mismatch. Among twenty random training instances, schedule shape modulates basin occupation on six of the thirteen multi-basin-in-readout instances, with dominant-configuration shifts of up to 38 percentage points including changes of the dominant configuration. A pre-registered linear predictor of schedule sensitivity from exhaustively computable landscape features fails on ten held-out instances, indicating that schedule sensitivity is not captured by simple linear functions of the tested landscape moments. The bracketing result revises an earlier two-pause-enhancement claim and reframes reverse-anneal schedules as instance-specific basin-occupation probes rather than universal quantum-enhancement knobs.
On a mixed-frustration 12-qubit Ising instance run on two D-Wave generations, Advantage2 Zephyr and Advantage_system6.4 Pegasus, the late-time subsystem autocorrelation under cycled reverse annealing sits strictly between two equilibrium reference processes at the device-calibrated effective temperature: localized parallel tempering, and delocalized equilibrated path-integral simulated quantum annealing at a fixed Advantage2 pause-point transverse-field scale. The bracket holds on all three tested schedules and at both hardware calibrations. We obtain this result through two ingredients: a cycled reverse-anneal protocol (reinitialize_state=False, 50 cycles per submission) used as a Markov-chain probe of the device's pause-point dynamics, and a parallel-tempering falsification framework with bias-corrected and accelerated bootstrap 95% confidence intervals. Of eighteen tested (instance, schedule) combinations on Advantage2, three are PT-unmatched and correspond to two distinct Ising instances; an independent native-graph control with no minor embedding on a third mixed-frustration instance reproduces the same direction of mismatch. Among twenty random training instances, schedule shape modulates basin occupation on six of the thirteen multi-basin-in-readout instances, with dominant-configuration shifts of up to 38 percentage points including changes of the dominant configuration. A pre-registered linear predictor of schedule sensitivity from exhaustively computable landscape features fails on ten held-out instances, indicating that schedule sensitivity is not captured by simple linear functions of the tested landscape moments. The bracketing result revises an earlier two-pause-enhancement claim and reframes reverse-anneal schedules as instance-specific basin-occupation probes rather than universal quantum-enhancement knobs.
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 with the total-variation distance 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<0.05, while a wrong-basin instance, reproduced at two Hamiltonian scales, passes the memory test yet reaches DTV>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.
Quadratic unconstrained binary optimization (QUBO) is the standard interface to quantum annealers, yet a single constrained task admits many QUBO encodings whose penalty choices reshape the energy landscape experienced by hardware. We study a Job Shop Scheduling instance using a two-parameter family of encodings controlled by penalty weights psum (one-hot/sum constraints) and ppair (precedence constraints). Sweeping (psum,ppair), we observe sharp transitions in feasibility and solver success across classical annealing-inspired heuristics and on a D-Wave Advantage processor. Going beyond solution probability, we treat the annealer as an open thermodynamic system and perform cyclic reverse-annealing experiments initialized from thermal samples, measuring the stochastic processor energy change. From the first two moments of this energy change we infer lower bounds on entropy production, work, and exchanged heat via thermodynamic uncertainty relations, and corroborate the observed trends with adiabatic master equation simulations. We find that the same encoding transitions that govern computational hardness also reorganize dissipation: weak penalties generate low-energy infeasible manifolds, while overly strong penalties suppress the effective problem energy scale and increase irreversibility, reducing the thermodynamic efficiency. Our results establish QUBO penalties as thermodynamic control knobs and motivate thermodynamics-aware encoding strategies for noisy intermediate-scale quantum annealers.
Annealing schedule control provides opportunities to better understand the manner and mechanisms by which putative quantum annealers operate. By appropriately modifying the annealing schedule to include a pause (keeping the Hamiltonian fixed) for a period of time, we show that it is possible to more directly probe the dissipative dynamics of the system at intermediate points along the anneal and examine thermal relaxation rates, for example, by observing the repopulation of the ground state after the minimum spectral gap. We provide a detailed comparison of experiments from a D-Wave device, simulations of the quantum adiabatic master equation, and a classical analogue of quantum annealing, spin-vector Monte Carlo, and we observe qualitative agreement, showing that the characteristic increase in success probability when pausing is not a uniquely quantum phenomena. We find that the relaxation in our system is dominated by a single timescale, which allows us to give a simple condition for when we can expect pausing to improve the time to solution, the relevant metric for classical optimization. Finally, we also explore in simulation the role of temperature whilst pausing as a means to better distinguish quantum and classical models of quantum annealers.
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.
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.
We evaluate using programmable superconducting flux qubit D-Wave quantum annealers to approximate the partition function of Ising models. We propose the use of two distinct quantum annealer sampling methods: chains of Monte Carlo-like reverse quantum anneals, and standard linear-ramp quantum annealing. The control parameters used to attenuate the quality of the simulations are the effective analog energy scale of the J coupling, the total annealing time, and for the case of reverse annealing the anneal-pause. The core estimation technique is to sample across the energy spectrum of the classical Hamiltonian of interest, and therefore obtain a density of states estimate for each energy level, which in turn can be used to compute an estimate of the partition function with some sampling error. This estimation technique is powerful because once the distribution is sampled it allows thermodynamic quantity computation at arbitrary temperatures. On a 25 spin ±J hardware graph native Ising model we find parameter regimes of the D-Wave processors that provide comparable result quality to two standard classical Monte Carlo methods, Multiple Histogram Reweighting and Wang-Landau. Remarkably, we find that fast quench-like anneals can quickly generate ensemble distributions that are very good estimates of the true partition function of the classical Ising model; on a Pegasus graph-structured QPU we report a logarithmic relative error of 7.6×10−6, from 171,000 samples generated using 0.2 seconds of QPU time with an anneal time of 8 nanoseconds per sample which is interestingly within the closed system dynamics timescale of the superconducting qubits.