Neural and Tensor Networks in the Study of Quantum Annealing Processors

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.