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arXiv:1905.13215 · IEEE International Conference on Rebooting Computing (ICRC)

Image Classification Using Quantum Inference on the D-Wave 2X

Nga T. T. Nguyen, Garrett T. Kenyon

Published Nov 1, 2018• 30 citations
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Abstract

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 built two deep convolutional neural networks (DCNNs). The first DCNN used an AlexNet-like architecture and the second a state-of-the-art residual network (RESNET)model, both implemented in TensorFlow. The two DCNNs yielded classification scores of 94.54 ± 0.7% and 98.8 ± 0.1%, respectively. As a control, we showed that both DCNN architectures 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 DCNN and contained 47 fully-connected features, 47 being the maximum number of dictionary elements that could be embedded onto the D-Wave 2X hardware. 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%. We found that the classification performance supported by quantum inference was maximal at an optimal level of sparsity corresponding to a critical value of the sparsity/reconstruction error trade-off parameter that previous work has associated with a second order phase transition, an observation supported by a free energy analysis of D-Wave energy states. We mimicked a transfer learning protocol by feeding the D-Wave representations into a multilayer perceptron (MLP), yielding 98.48% classification performance. The classification performance supported by a single-layer of quantum inference was superior to that supported by a classical matching pursuit algorithm set to the same level of sparsity. Whereas the classification performance of both DCNNs declined as the number of training examples was reduced, the classification performance supported by quantum inference was insensitive to the number of training examples. We thus conclude that quantum inference supports classification of reduced dimensional MNIST images exceeding that of a size-matched AlexNet-like DCNN and nearly equivalent to a state-of-the-art RESNET DCNN.

DOI
10.1109/icrc.2018.8638596

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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 built two deep convolutional neural networks (DCNNs). The first DCNN used an AlexNet-like architecture and the second a state-of-the-art residual network (RESNET)model, both implemented in TensorFlow. The two DCNNs yielded classification scores of 94.54 ± 0.7% and 98.8 ± 0.1%, respectively. As a control, we showed that both DCNN architectures 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 DCNN and contained 47 fully-connected features, 47 being the maximum number of dictionary elements that could be embedded onto the D-Wave 2X hardware. 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%. We found that the classification performance supported by quantum inference was maximal at an optimal level of sparsity corresponding to a critical value of the sparsity/reconstruction error trade-off parameter that previous work has associated with a second order phase transition, an observation supported by a free energy analysis of D-Wave energy states. We mimicked a transfer learning protocol by feeding the D-Wave representations into a multilayer perceptron (MLP), yielding 98.48% classification performance. The classification performance supported by a single-layer of quantum inference was superior to that supported by a classical matching pursuit algorithm set to the same level of sparsity. Whereas the classification performance of both DCNNs declined as the number of training examples was reduced, the classification performance supported by quantum inference was insensitive to the number of training examples. We thus conclude that quantum inference supports classification of reduced dimensional MNIST images exceeding that of a size-matched AlexNet-like DCNN and nearly equivalent to a state-of-the-art RESNET DCNN.
Understanding how the D-Wave quantum computer could be used for machine learning problems is of growing interest. Our work explores the feasibility of using the D-Wave as a sampler for a machine learning task. We describe a hybrid method that combines a classical deep neural network autoencoder with a quantum annealing Restricted Boltzmann Machine (RBM) using the D-Wave for image generation. Our method overcomes two key limitations in the 2000-qubit D-Wave processor, namely the limited number of qubits available to accommodate typical problem sizes for fully connected quantum objective functions, and samples that are binary pixel representations. As a consequence of these limitations we are able to show how we achieved nearly a 22-fold compression factor of grayscale 28 x 28 sized images to binary 6 x 6 sized images with a lossy recovery of the original 28 x 28 grayscale images. We further show how generating samples from the D-Wave after training the RBM, resulted in 28 x 28 images that were variations of the original input data distribution, as opposed to recreating the training samples. We evaluated the quality of this method by using a downstream classification method. We formulated a MNIST classification problem using a deep convolutional neural network that used samples from the quantum RBM to train the MNIST classifier and compared the results with a MNIST classifier trained with the original MNIST training data set, as well as a MNIST classifier trained using classical RBM samples. We also explored using a secondary dataset, the MNIST Fashion dataset and demonstrate the first quantum-generated fashion. Our hybrid autoencoder approach indicates advantage for RBM results relative to the use of a current RBM classical computer implementation for image-based machine learning and even more promising results for the next generation D-Wave quantum system. Our method for compression and image mappings is not constrained to RBMs, the autoencoder part of this method could be coupled with other quantum-based algorithms.
We use a quantum annealing D-Wave 2X (1,152-qubit) computer to generate sparse representations of Canny-filtered, center-cropped 30×30 CIFAR-10 images. Each binary neuron (qubit) represents a feature kernel obtained initially by imprinting on a randomly chosen 5×5 image patch and then adapted via an off-line Hebbian learning protocol using the sparse solutions generated by the D-Wave. When using binary neurons, the energy function is non-convex (multiple local-minima) and finding a global minimum is NP-hard. Quantum annealing provides a strategy for finding sparse representations that correspond to good local minima of a non-convex cost function. To overcome the severe coupling restrictions between physical qubits on the D-Wave Chimera graph, we use embedding tools to achieve approximately all-to-all connectivity across a reduced number of logical qubits. We assess the sparse representations generated by the D-Wave using both the total energy as well as classification accuracy on a subset of the CIFAR-10 database. The D-Wave 2X outperforms two classical state-of-the-art binary solvers, GUROBI and Chimera-inspired algorithm Hamze-Freitas-Selby (HFS). Specifically, the D-Wave 2X yields lower energy sparse solutions within seconds while the largest problems take over 10 hours for both GUROBI and HFS. We obtained cross-validation classification of 31.02% for the first 4K images using 47 features on the quantum D- Wave 2X.
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 CCC-class problem into CCC independent QUBOs, each with (d+1)K(d+1)K(d+1)K binary variables, where ddd is the feature dimension and KKK 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.
In order to leverage quantum computers for machine learning tasks such as image classification, consideration is required. Noisy Intermediate-Scale Quantum (NISQ) computers have limitations that include noise, scalability, read-in and read-out times, and gate operation times. Therefore, strategies should be devised to mitigate the impact complex datasets that can have on the overall efficiency of a quantum machine learning pipeline. This may otherwise lead to excessive resource demands or noise. We apply a classical feature extraction using a ResNet10-inspired convolutional autoencoder to reduce dataset dimensionality and extract abstract, meaningful features before feeding them into a quantum layer. The chosen quantum layer is a quantum-enhanced support vector machine (QSVM), as SVMs typically do not require large sample sizes to identify patterns in data and have short-depth quantum circuits, which limits the impact of noise. The autoencoder is trained to extract meaningful features through image reconstruction, aiming to minimize the mean squared error across a training set of images. We use three datasets to illustrate the pipeline: HTRU-1, MNIST, and CIFAR-10. We include a quantum-enhanced one-class support vector machine (QOCSVM) for the highly unbalanced HTRU-1 set, with classical machine learning results for comparison. HTRU-2 is also included to serve as a benchmark for a dataset with meaningful features. The autoencoder achieved near-perfect reconstruction and high accuracy for MNIST, while CIFAR-10 showed poorer performance due to image complexity, and HTRU-1 struggled due to the imbalance in the dataset. The varying performance across datasets highlights the need to balance dimensionality reduction and prediction performance using quantum methods.
Image classification plays a vital role in large-scale data analysis, especially in object recognition tasks using advanced Deep Learning (DL) frameworks. However, the growing complexity and computational demands of modern DL models have introduced challenges related to scalability and efficiency. Quantum Computing (QC) has emerged as a promising alternative, capable of addressing these limitations by leveraging the principles of Quantum Machine Learning (QML). However, many existing QML models require a large number of qubits, which poses limitations within the current Noisy Intermediate-Scale Quantum (NISQ) era. This work introduces a novel Adaptive Quantum Convolutional Neural Network (AQCNN) designed for efficient and scalable image classification within the constraints of NISQ devices. Addressing the limitations of existing QML approaches, particularly the high qubit requirements, AQCNN incorporates a resource-efficient quantum convolutional layer that performs localized quantum filtering using parameterized quantum circuits. A classical preprocessing layer encodes input features to reduce qubit load, followed by quantum embedding and hybrid quantum-classical layers that optimize feature extraction and classification performance. The model leverages an adaptive quantum convolution strategy, minimizing quantum gate depth and circuit complexity while preserving critical spatial hierarchies in image data. Evaluated on benchmark datasets, AQCNN achieved 95.88% accuracy on MNIST and 95.68% on FMNIST, outperforming comparable QML architectures. Additionally, the model supports scalable execution through parallel quantum circuit arrays, enabling practical deployment on current quantum hardware. This architecture demonstrates a significant advance in quantum-assisted image classification, balancing performance with qubit and gate efficiency. The integration of adaptive quantum convolution and hybrid processing not only enhances classification accuracy but also provides a viable path forward for deploying QML solutions under realistic hardware constraints.