Quantum annealers natively minimize quadratic unconstrained binary optimization (QUBO) problems, yet faithfully compiling continuous convex objectives into discrete binary forms with formal guarantees remains challenging. We present a complete, algebraically verifiable pipeline for training a linear squared-hinge support vector machine on quantum annealing hardware. The construction comprises four stages with rigorous justification: (i) an exact epigraph reformulation eliminating the hinge nonlinearity, (ii) equality conversion via surplus variables with a quadratic penalty whose exactness on the finite binary domain is formally established, (iii) closed-form QUBO coefficients and a provably energy-preserving Ising mapping, and (iv) a moment-based three-component decoder that reconstructs continuous parameters from noisy annealer samples using empirical first- and second-order statistics. We execute this pipeline end-to-end on D-Wave Advantage systems and evaluate under a rigorous protocol with 30 stratified splits, bootstrap confidence intervals, paired tests, and effect sizes. The feature-wise solver achieves 87-89% test accuracy on the Iris benchmark, competitive with classical baselines at this scale. We contribute a fully auditable reduction from convex SVM training to Ising optimization rather than claiming quantum advantage, and explicitly characterize limitations from discretization, embedding overhead, and feature-wise decomposition.
This work presents a fully quantum approach to support vector machine (SVM) learning by integrating gate-based quantum kernel methods with quantum annealing-based optimization. We explore the construction of quantum kernels using various feature maps and qubit configurations, evaluating their suitability through Kernel-Target Alignment (KTA). The SVM dual problem is reformulated as a Quadratic Unconstrained Binary Optimization (QUBO) problem, enabling its solution via quantum annealers. Our experiments demonstrate that a high degree of alignment in the kernel and an appropriate regularization parameter lead to competitive performance, with the best model achieving an F1-score of 90%. These results highlight the feasibility of an end-to-end quantum learning pipeline and the potential of hybrid quantum architectures in quantum high-performance computing (QHPC) contexts.
This paper presents an Optuna-based formulation-level auto-tuning framework for support vector machines (SVMs) implemented on multiple quantum-inspired annealers. In an annealing-based SVM, continuous dual variables are discretized and converted into a quadratic unconstrained binary optimization (QUBO) model. This transformation introduces three coupled classes of parameters: representation parameters-the encoding base B and bit depth K-which determine numerical range, resolution, and QUBO size; the RBF kernel parameter γ, which determines classifier geometry; and the equality-constraint penalty ξ, which controls feasibility and coefficient balance. We formulate their joint selection as a mixed discrete-continuous black-box optimization problem. The framework has two optimization levels: an inner annealer minimizes the generated QUBO, while an outer Optuna loop reconstructs the formulation in every trial and maximizes validation accuracy. The same solver-agnostic procedure is applied to Fixstars Amplify Annealing Engine, Toshiba SQBM+, and Fujitsu Digital Annealer using TPE and Gaussian-process samplers and is compared with conventional grid search. Experiments on linear and nonlinear classification tasks with 0-20% label noise show mean gains over grid search of approximately 0.8 and 2.1 percentage points, respectively. The results demonstrate that formulation quality and backend capability must be evaluated jointly and that task-level feedback can compensate for discretization, penalty imbalance, and backend-dependent approximate optimization.
Variational quantum circuits for image classification suffer from barren plateaus, while quantum kernel methods scale quadratically with dataset size. We propose an iterative framework based on Quadratic Unconstrained Binary Optimization (QUBO) for training the classifier head of convolutional neural networks (CNNs) via quantum annealing, entirely avoiding gradient-based circuit optimization. Following the Extreme Learning Machine paradigm, convolutional filters are randomly initialized and frozen, and only the fully connected layer is optimized. At each iteration, a convex quadratic surrogate derived from the feature Gram matrix replaces the non-quadratic cross-entropy loss, yielding an iteration-stable curvature proxy. A per-output decomposition splits the
C-class problem into
C independent QUBOs, each with
(d+1)K binary variables, where
d is the feature dimension and
K is the bit precision, so that problem size depends on the image resolution and bit precision, not on the number of training samples. We evaluate the method on six image-classification benchmarks (sklearn digits, MNIST, Fashion-MNIST, CIFAR-10, EMNIST, KMNIST). A precision study shows that accuracy improves monotonically with bit resolution, with 10 bits representing a practical minimum for effective optimization; the 15-bit formulation remains within the qubit and coupler limits of current D-Wave Advantage hardware. The 20-bit formulation matches or exceeds classical stochastic gradient descent on MNIST, Fashion-MNIST, and EMNIST, while remaining competitive on CIFAR-10 and KMNIST. All experiments use simulated annealing, establishing a baseline for direct deployment on quantum annealing hardware.
We present a novel slack-free, penalty-based framework for reformulating constrained binary optimization as Quadratic Unconstrained Binary Optimization (QUBO) on near-term quantum annealing hardware. Given a user-chosen penalty function that most naturally captures a constraint---typically non-quadratic, such as a Heaviside-function surrogate---and a target probability measure over the Boolean hypercube, our method returns the weighted least-squares projection of the chosen penalty function onto the subspace spanned by linear and quadratic Walsh--Fourier characters that correspond to physically realizable couplings on the target hardware graph. Within this restricted family, the resulting quadratic surrogate is uniquely and optimally determined by the normal equations: unlike state-of-the-art approaches, it introduces no per-constraint penalty coefficients to tune and avoids dense all-pairs couplings by construction. Two practical consequences follow. First, the projected penalty respects device connectivity, reducing chain lengths and physical-qubit overhead after minor embedding. Second, we show empirically that this hardware-native surrogate can outperform denser full-pairwise projections, despite being drawn from a strictly smaller approximation space. This advantage widens once the QUBO is embedded and sampled on quantum annealers, yielding samples with the lowest worst-case and mean objective gaps compared to unbalanced penalization and a hardware-blind projection onto all quadratic terms.
This paper proposes an integrated QUBO-based quantum-annealing optimization framework for next-generation cloud computing. First, for resource-demand forecasting, we blend Autoregressive (AR) models with Quadratic Unconstrained Binary Optimization (QUBO) and solve the resulting problem via Simulated Annealing; monthly-scale tests reveal superior trend-capture accuracy compared with classical predictors. Second, we embed quantum optimization into Support Vector Machines by casting kernel selection and penalty-parameter tuning as QUBO instances; evaluations on the Iris benchmark—and on synthetically enlarged variants—show marked gains in both classification accuracy and training speed, especially under large-data regimes. Third, we extend the same paradigm to deep learning: a QUBO-formulated quantum-annealing routine optimizes weight initialization and layer-wise learning rates in convolutional networks for image classification, yielding higher top-1 accuracy and reduced wall-clock training time. Across all tasks the hybrid quantum-classical solver consistently outperforms its classical counterparts while maintaining linear scalability in cloud environments. These results show the practical potential of quantum - enhanced algorithms for resource prediction, classification, and deep learning, and pave the way for wider use of quantum technologies in cloud - based AI services.
The training loss of binary and ternary neural networks, expanded as a multilinear polynomial over the discrete weights, is structurally equivalent to the energy of a hierarchical high-order Ising model. We exploit this equivalence to apply Ising solvers to discrete-weight network training, while accounting for a fundamental difference in objectives: an Ising solver seeks the ground state of a fixed energy function, whereas training seeks solutions that generalize to unseen data. Our key contribution is
ΣΔ-Sampler, an optimizer that reconciles these objectives by embedding a stochastic sampling-and-annealing step as a noisy quantizer inside a first-order
ΣΔ noise-shaping loop. The loop pushes noise from weight quantization, high-order frustration, and mini-batch sampling out of the low-frequency adaptation band, so that discrete weight updates follow the smooth descent trajectories embedded in the rugged loss landscape. We validate the framework on a planted quadratic unconstrained binary optimization (QUBO) benchmark with a known minimizer; on CIFAR-10, where a
13M-parameter ternary model comes within
1% of full-precision accuracy; on ImageNet-1k, where a ternary ResNet-18 comes within
0.4% Top-5 accuracy of a ternary baseline; on class-incremental continual learning, where prior-task accuracy is preserved; and on MatMul-free language models up to
2.7B parameters, where it outperforms a straight-through-estimator baseline under matched continued pre-training. Compared with standard quantization-aware training,
ΣΔ-Sampler reduces the training memory footprint by over
50%, delivers an order-of-magnitude speed-up, and reduces weight-update memory traffic by four orders of magnitude, making it attractive for on-device training and fine-tuning of large binary and ternary models.