# Image classification using quantum inference on the D-Wave 2X

arXiv: https://arxiv.org/abs/1905.13215 · HTML: https://mlsanity.com/paper/1905.13215/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2019.

## Built on by (most cited first, 15 of 15)

- [Recent advances for quantum classifiers](https://mlsanity.com/paper/2108.13421/) (2021)
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- [Adiabatic Quantum Graph Matching with Permutation Matrix Constraints](https://mlsanity.com/paper/2107.04032/) (2021)
- [A Hybrid Quantum-Classical Algorithm for Robust Fitting](https://mlsanity.com/paper/2201.10110/) (2022)
- [QUILT: Effective Multi-Class Classification on Quantum Computers Using an Ensemble of Diverse Quantum Classifiers](https://mlsanity.com/paper/2309.15056/) (2023)
- [Q-FW: A Hybrid Classical-Quantum Frank-Wolfe for Quadratic Binary Optimization](https://mlsanity.com/paper/2203.12633/) (2022)
- [A Review of Machine Learning Classification Using Quantum Annealing for Real-world Applications](https://mlsanity.com/paper/2106.02964/) (2021)
- [Robust Fitting on a Gate Quantum Computer](https://mlsanity.com/paper/2409.02006/) (2024)
- [Lossy compression of statistical data using quantum annealer](https://mlsanity.com/paper/2110.02142/) (2021)
- [Nonnegative/Binary Matrix Factorization for Image Classification using Quantum Annealing](https://mlsanity.com/paper/2311.01028/) (2023)
- [QuAnt: Quantum Annealing with Learnt Couplings](https://mlsanity.com/paper/2210.08114/) (2022)
- [Prediction and compression of lattice QCD data using machine learning algorithms on quantum annealer](https://mlsanity.com/paper/2112.02120/) (2021)
- [Comparing Quantum Annealing and Spiking Neuromorphic Computing for Sampling Binary Sparse Coding QUBO Problems](https://mlsanity.com/paper/2405.20525/) (2024)
- [Layer-wise QUBO-Based Training of CNN Classifiers for Quantum Annealing](https://mlsanity.com/paper/2603.02958/) (2026)

## Abstract (arXiv)

We use a quantum annealing D-Wave 2X computer to obtain solutions to NP-hard sparse coding problems. To reduce the dimensionality of the sparse coding problem to fit on the quantum D-Wave 2X hardware, we passed downsampled MNIST images through a bottleneck autoencoder. To establish a benchmark for classification performance on this reduced dimensional data set, we used an AlexNet-like architecture implemented in TensorFlow, obtaining a classification score of 94.54 ± 0.7 %. As a control, we showed that the same AlexNet-like architecture produced near-state-of-the-art classification performance (~ 99%) on the original MNIST images. To obtain a set of optimized features for inferring sparse representations of the reduced dimensional MNIST dataset, we imprinted on a random set of 47 image patches followed by an off-line unsupervised learning algorithm using stochastic gradient descent to optimize for sparse coding. Our single-layer of sparse coding matched the stride and patch size of the first convolutional layer of the AlexNet-like deep neural network and contained 47 fully-connected features, 47 being the maximum number of dictionary elements that could be embedded onto the D-Wave 2X hardware. Recent work suggests that the optimal level of sparsity corresponds to a critical value of the trade-off parameter associated with a putative second order phase transition, an observation supported by a free energy analysis of D-Wave energy states. When the sparse representations inferred by the D-Wave 2X were passed to a linear support vector machine, we obtained a classification score of 95.68%. Thus, on this problem, we find that a single-layer of quantum inference is able to outperform a standard deep neural network architecture.