[2603.02958] Layer-wise QUBO-Based Training of CNN Classifiers for Quantum Annealing

Quantum Physics arXiv:2603.02958 (quant-ph) [Submitted on 3 Mar 2026] Title:Layer-wise QUBO-Based Training of CNN Classifiers for Quantum Annealing Authors:Mostafa Atallah, Rebekah Herrman View a PDF of the paper titled Layer-wise QUBO-Based Training of CNN Classifiers for Quantum Annealing, by Mostafa Atallah and 1 other authors View PDF HTML (experimental) Abstract: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...