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

arXiv: https://arxiv.org/abs/2603.02958 · HTML: https://mlsanity.com/paper/2603.02958/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 59 references that are in the map.
- First posted on arXiv 3 Mar 2026.

## Builds on (most cited first, 21 of 21)

- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Transfer learning in hybrid classical-quantum neural networks](https://mlsanity.com/paper/1912.08278/) (2019)
- [The Inductive Bias of Quantum Kernels](https://mlsanity.com/paper/2106.03747/) (2021)
- [Quantum machine learning for image classification](https://mlsanity.com/paper/2304.09224/) (2023)
- [QUBO Formulations for Training Machine Learning Models](https://mlsanity.com/paper/2008.02369/) (2020)
- [Quantum-Assisted Learning of Hardware-Embedded Probabilistic Graphical Models](https://mlsanity.com/paper/1609.02542/) (2016)
- [Image classification using quantum inference on the D-Wave 2X](https://mlsanity.com/paper/1905.13215/) (2019)
- [QUILT: Effective Multi-Class Classification on Quantum Computers Using an Ensemble of Diverse Quantum Classifiers](https://mlsanity.com/paper/2309.15056/) (2023)
- [Restricted Boltzmann Machines for galaxy morphology classification with a quantum annealer](https://mlsanity.com/paper/1911.06259/) (2019)
- [A Hybrid Quantum enabled RBM Advantage: Convolutional Autoencoders For Quantum Image Compression and Generative Learning](https://mlsanity.com/paper/2001.11946/) (2020)
- [Nonnegative/Binary Matrix Factorization for Image Classification using Quantum Annealing](https://mlsanity.com/paper/2311.01028/) (2023)
- [Lean classical-quantum hybrid neural network model for image classification](https://mlsanity.com/paper/2412.02059/) (2024)
- [Towards Transfer Learning for Large-Scale Image Classification Using Annealing-based Quantum Boltzmann Machines](https://mlsanity.com/paper/2311.15966/) (2023)
- [Multi-Class Quantum Convolutional Neural Networks](https://mlsanity.com/paper/2404.12741/) (2024)
- [Optimization of the quantization of dense neural networks from an exact QUBO formulation](https://mlsanity.com/paper/2510.16075/) (2025)

## Abstract (arXiv)

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.