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

TL;DR

This paper introduces a QUBO-based iterative training framework for CNN classifiers that leverages quantum annealing, avoiding gradient-based optimization and scaling efficiently with dataset size, showing promising results on multiple benchmarks.

Contribution

It presents a novel QUBO formulation for training CNN classifier heads using quantum annealing, bypassing gradient-based methods and enabling scalable, hardware-compatible optimization.

Findings

Accuracy improves with higher bit resolution, with 10 bits being effective.

20-bit formulation matches or exceeds classical SGD on several datasets.

Method is feasible within current quantum annealing hardware constraints.

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, 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.