Generalization ability is essential for assessing the robustness of quantum steerability classifiers. In this work, we investigate robust steerability classification from the perspective of key feature extraction and matrix structure preservation. The dataset introduced in Phys. Rev. A 100, 022314 (2019) provides the training basis for the present work. With strictly unsteerable random states, T-diagonal states, and All-Versus-Nothing (AVN) states, we evaluate the generalization performance of support vector machines (SVMs), multilayer perceptrons (MLPs), and deep perceptron control classifiers(DPs) trained on full-information features. None of these classifiers perform consistently on T-diagonal or AVN states. Given that stochastic local operations and classical communication and local unitary transformations preserve steerability, we introduce a key feature that determines steerability. SVMs trained on this feature overcome the instability on T-diagonal states but still fail on AVN states. Moreover, this feature alone is insufficient for training robust neural-network-based steerability classifiers. Recognizing that flattening quantum states into one-dimensional vectors may destroy their intrinsic matrix structure, we introduce matrix versions of both features and train convolutional neural networks on them. The most robust overall performance among the tested classifiers is achieved only when the matrix structure is preserved and key features are extracted simultaneously. Finally, as an application, we employ the most robust classifiers to predict the number of projective measurements required to detect the steerability of axially symmetric states
Generalization ability is essential for assessing the robustness of quantum steerability classifiers. In this work, we investigate robust steerability classification from the perspective of key feature extraction and matrix structure preservation. The dataset introduced in Phys. Rev. A 100, 022314 (2019) provides the training basis for the present work. With strictly unsteerable random states, T-diagonal states, and All-Versus-Nothing (AVN) states, we evaluate the generalization performance of support vector machines (SVMs), multilayer perceptrons (MLPs), and deep perceptron control classifiers(DPs) trained on full-information features. None of these classifiers perform consistently on T-diagonal or AVN states. Given that stochastic local operations and classical communication and local unitary transformations preserve steerability, we introduce a key feature that determines steerability. SVMs trained on this feature overcome the instability on T-diagonal states but still fail on AVN states. Moreover, this feature alone is insufficient for training robust neural-network-based steerability classifiers. Recognizing that flattening quantum states into one-dimensional vectors may destroy their intrinsic matrix structure, we introduce matrix versions of both features and train convolutional neural networks on them. The most robust overall performance among the tested classifiers is achieved only when the matrix structure is preserved and key features are extracted simultaneously. Finally, as an application, we employ the most robust classifiers to predict the number of projective measurements required to detect the steerability of axially symmetric states
The rapid growth of computer vision and increasingly complex image recognition tasks has exposed fundamental computational limitations of classical machine learning models, motivating the exploration of quantum computing as an emerging new paradigm. This paper presents a comprehensive benchmarking study of classical and quantum machine learning models for image recognition on the MNIST handwritten digit dataset, evaluating both traditional models, a Classical Support Vector Machine (CSVM) and a Quantum Support Vector Machine (QSVM), and deep neural network models, a Classical Convolutional Neural Network (CCNN) and a Quantum Convolutional Neural Network (QCNN), across four performance dimensions: classification accuracy, computational runtime, parameter count, and memory requirements. Experiments are conducted as functions of both feature dimensionality and sample size, and across CPU and GPU execution environments, providing a controlled, multidimensional comparison to address gaps in prior work. For the SVM-based models, QSVM consistently outperforms CSVM in accuracy, reaching ∼ 0.90 versus ∼ 0.85 at 1,000 samples, with a higher computational cost. A feature count of 10 qubits and a sample size in the range of 200 -- 500 emerge as practical operating points that balance accuracy and runtime. For the neural network models, CCNN and QCNN achieve comparable classification accuracy, both exceeding 0.96 at 64 features and 60,000 samples, yet QCNN offers superior parameter and memory efficiency at higher feature counts, while incurring higher runtime. Across both model families, quantum models consistently outperform classical models by greater margins in accuracy as feature dimensionality or sample size increases.
Quantum computing (QC) has opened the door to advancements in machine learning (ML) tasks that are currently implemented in the classical domain. Convolutional neural networks (CNNs) are classical ML architectures that exploit data locality and possess a simpler structure than a fully connected multi-layer perceptrons (MLPs) without compromising the accuracy of classification. However, the concept of preserving data locality is usually overlooked in the existing quantum counterparts of CNNs, particularly for extracting multifeatures in multidimensional data. In this paper, we present an multidimensional quantum convolutional classifier (MQCC) that performs multidimensional and multifeature quantum convolution with average and Euclidean pooling, thus adapting the CNN structure to a variational quantum algorithm (VQA). The experimental work was conducted using multidimensional data to validate the correctness and demonstrate the scalability of the proposed method utilizing both noisy and noise-free quantum simulations. We evaluated the MQCC model with reference to reported work on state-of-the-art quantum simulators from IBM Quantum and Xanadu using a variety of standard ML datasets. The experimental results show the favorable characteristics of our proposed techniques compared with existing work with respect to a number of quantitative metrics, such as the number of training parameters, cross-entropy loss, classification accuracy, circuit depth, and quantum gate count.
In order to leverage quantum computers for machine learning tasks such as image classification, careful consideration is required: NISQ-era quantum computers have limitations, which include noise, scalability, read-in and read-out times, and gate operation times. Therefore, strategies should be devised to mitigate the impact that complex datasets can have on the overall efficiency of a quantum machine learning pipeline. This may otherwise lead to excessive resource demands or increased noise. We apply a classical feature extraction method using a ResNet10-inspired convolutional autoencoder to both reduce the dimensionality of the dataset and extract abstract and meaningful features before feeding them into a quantum machine learning block. The quantum block of choice is a quantum-enhanced support vector machine (QSVM), as support vector machines 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. Three image datasets are used to illustrate the pipeline: HTRU-1, MNIST, and CIFAR-10. We also include a quantum-enhanced one-class support vector machine (QOCSVM) for the highly unbalanced HTRU-1 set, as well as classical machine learning results to serve as a benchmark. Finally, the HTRU-2 dataset is also included to serve as a benchmark for a dataset with well-correlated features. The autoencoder achieved near-perfect reconstruction and high classification accuracy for MNIST, while CIFAR-10 showed poorer performance due to image complexity, and HTRU-1 struggled because of dataset imbalance. This highlights the need for a balance between dimensionality reduction through classical feature extraction and prediction performance using quantum methods.
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.
Adversarial robustness and generalization are both crucial properties of reliable machine learning models. In this paper, we study these properties in the context of quantum machine learning based on Lipschitz bounds. We derive parameter-dependent Lipschitz bounds for quantum models with trainable encoding, showing that the norm of the data encoding has a crucial impact on the robustness against data perturbations. Further, we derive a bound on the generalization error which explicitly involves the parameters of the data encoding. Based on these theoretical results, we propose a practical strategy for training robust and generalizable quantum models by regularizing the Lipschitz bound in the cost. Moreover, we show that, for fixed and nontrainable encodings, as those frequently employed in quantum machine learning, the Lipschitz bound cannot be influenced by tuning the parameters. Thus trainable encodings are crucial for systematically adapting robustness and generalization during training. The practical implications of our theoretical findings are illustrated with numerical results. Published by the American Physical Society 2024
Abstract Generalization is essential for reliable machine-learning detection of quantum steerability. In this work, we develop a CNN-based approach using the matrix versions of the full-information feature F 1 and the steering-determined feature F 2 as inputs for two-qubit steerability classification. Several physically distinct state families with reliable labels are employed to evaluate classifier generalization. Vector-input classifiers based on F 1 and F 2 are included as benchmarks under a unified classification protocol. Across the considered classifiers and test datasets, F 2 -based models exhibit consistently more stable generalization than their F 1 -based counterparts, indicating that steering-determined feature extraction plays a more dominant role than classifier selection in the observed performance improvement in the considered settings. Meanwhile, no single classifier is uniformly optimal across all physical state families. Since CNN– F 2 achieves the best overall performance on the T -diagonal benchmarks, it is further employed to visualize and estimate the projective-measurement steering hierarchy of axially symmetric states, a special subclass of T -diagonal states.