Image processing is one of the most promising applications for quantum machine learning (QML). Quanvolutional Neural Networks with non-trainable parameters are the preferred solution to run on current and near future quantum devices. The typical input preprocessing pipeline for quanvolutional layers comprises of four steps: optional input binary quantization, encoding classical data into quantum states, processing the data to obtain the final quantum states, decoding quantum states back to classical outputs. In this paper we propose two ways to enhance the efficiency of quanvolutional models. First, we propose a flexible data quantization approach with memoization, applicable to any encoding method. This allows us to increase the number of quantization levels to retain more information or lower them to reduce the amount of circuit executions. Second, we introduce a new integrated encoding strategy, which combines the encoding and processing steps in a single circuit. This method allows great flexibility on several architectural parameters (e.g., number of qubits, filter size, and circuit depth) making them adjustable to quantum hardware requirements. We compare our proposed integrated model with a classical convolutional neural network and the well-known rotational encoding method, on two different classification tasks. The results demonstrate that our proposed model encoding exhibits a comparable or superior performance to the other models while requiring fewer quantum resources.
A successful Machine Learning (ML) model implementation requires three main components: training dataset, suitable model architecture and training procedure. Given dataset and task, finding an appropriate model might be challenging. AutoML, a branch of ML, focuses on automatic architecture search -- a meta method that aims at moving human from ML system design process. The success of ML and the development of quantum computing (QC) in recent years led to a birth of new fascinating field called Quantum Machine Learning (QML) that, amongst others, incorporates quantum computers into ML models. In this paper we present AQMLator, an Auto Quantum Machine Learning platform that aims to automatically propose and train the quantum layers of an ML model with minimal input from the user. This way, data scientists can bypass the entry barrier for QC and use QML. AQMLator uses standard ML libraries, making it easy to introduce into existing ML pipelines.
Quantum computing with qudits, an extension of qubits to multiple levels, is a research field less mature than qubit-based quantum computing. However, qudits can offer some advantages over qubits, by representing information with fewer separated components. In this article, we present QuForge, a Python-based library designed to simulate quantum circuits with qudits. This library provides the necessary quantum gates for implementing quantum algorithms, tailored to any chosen qudit dimension. Built on top of differentiable frameworks, QuForge supports execution on accelerating devices such as GPUs and TPUs, significantly speeding up simulations. It also supports sparse operations, leading to a reduction in memory consumption compared to other libraries. Additionally, by constructing quantum circuits as differentiable graphs, QuForge facilitates the implementation of quantum machine learning algorithms, enhancing the capabilities and flexibility of quantum computing research.
Quantum Machine Learning (QML) is considered one of the most promising applications of Quantum Computing in the Noisy Intermediate Scale Quantum (NISQ) era for the impact it is thought to have in the near future. Although promising theoretical assumptions, the exploration of how QML could foster new discoveries in Medicine and Biology fields is still in its infancy with few examples. In this study, we aimed to assess whether Quantum Kernels (QK) could effectively classify subtypes of Breast Cancer (BC) patients on the basis of molecular characteristics. We performed an heuristic exploration of encoding configurations with different entanglement levels to determine a trade-off between kernel expressivity and performances. Our results show that QKs yield comparable clustering results with classical methods while using fewer data points, and are able to fit the data with a higher number of clusters. Additionally, we conducted the experiments on the Quantum Processing Unit (QPU) to evaluate the effect of noise on the outcome. We found that less expressive encodings showed a higher resilience to noise, indicating that the computational pipeline can be reliably implemented on the NISQ devices. Our findings suggest that QK methods show promises for application in Precision Oncology, especially in scenarios where the dataset is limited in size and a granular non-trivial stratification of complex molecular data cannot be achieved classically.
Recent years have seen significant growth of quantum technologies, and specifically quantum sensing, both in terms of the capabilities of advanced platforms and their applications. One of the leading platforms in this context is nitrogen-vacancy (NV) color centers in diamond, providing versatile, high-sensitivity, and high-spatial-resolution magnetic sensing. Nevertheless, current schemes for spin resonance magnetic sensing (as applied by NV quantum sensing) suffer from tradeoffs associated with sensitivity, dynamic range, and bandwidth. Here we address this issue, and implement machine learning tools to enhance NV magnetic sensing in terms of the sensitivity/bandwidth tradeoff in large dynamic range scenarios. Our results indicate a potential reduction of required data points by at least a factor of 3, while maintaining the current error level. Our results promote quantum machine learning protocols for sensing applications towards more feasible and efficient quantum technologies.
Based on the linearity of quantum unitary operations, we propose a method that runs the parameterized quantum circuits before encoding the input data. This enables a dataset owner to train machine learning models on quantum cloud computation platforms, without the risk of leaking the information about the data. It is also capable of encoding a vast amount of data effectively at a later time using classical computations, thus saving runtime on quantum computation devices. The trained quantum machine learning models can be run completely on classical computers, meaning the dataset owner does not need to have any quantum hardware, nor even quantum simulators. Moreover, our method mitigates the encoding bottleneck by reducing the required circuit depth from $O(2^{n})$ to $O(n)$, and relax the tolerance on the precision of the quantum gates for the encoding. These results demonstrate yet another advantage of quantum and quantum-inspired machine learning models over existing classical neural networks, and broaden the approaches to data security.
Quantum computing promises to revolutionize machine learning, offering significant efficiency gains in tasks such as clustering and distance estimation. Additionally, it provides enhanced security through fundamental principles like the measurement postulate and the no-cloning theorem, enabling secure protocols such as quantum teleportation and quantum key distribution. While advancements in secure quantum machine learning are notable, the development of secure and distributed quantum analogues of kernel-based machine learning techniques remains underexplored. In this work, we present a novel approach for securely computing common kernels, including polynomial, radial basis function (RBF), and Laplacian kernels, when data is distributed, using quantum feature maps. Our methodology introduces a robust framework that leverages quantum teleportation to ensure secure and distributed kernel learning. The proposed architecture is validated using IBM's Qiskit Aer Simulator on various public datasets.
Quantum-enhanced machine learning is a rapidly evolving field that aims to leverage the unique properties of quantum mechanics to enhance classical machine learning. However, the practical applicability of these methods remains an open question, particularly beyond the context of specifically-crafted toy problems, and given the current limitations of quantum hardware. This study focuses on quantum kernel methods in the context of classification tasks. In particular, it examines the performance of Quantum Kernel Estimation (QKE) and Quantum Kernel Training (QKT) in connection with two quantum feature mappings, namely ZZFeatureMap and CovariantFeatureMap. Remarkably, these feature maps have been proposed in the literature under the conjecture of possible near-term quantum advantage and have shown promising performance in ad-hoc datasets. In this study, we aim to evaluate their versatility and generalization capabilities in a more general benchmark, encompassing both artificial and established reference datasets. Classical machine learning methods, specifically Support Vector Machines (SVMs) and logistic regression, are also incorporated as baseline comparisons. Experimental results indicate that quantum methods exhibit varying performance across different datasets. Despite outperforming classical methods in ad-hoc datasets, mixed results are obtained for the general case among standard classical benchmarks. Our experiments call into question a general added value of applying QKT optimization, for which the additional computational cost does not necessarily translate into improved classification performance. Instead, it is suggested that a careful choice of the quantum feature map in connection with proper hyperparameterization may prove more effective.
We introduce the novel class $(E_\alpha)_{\alpha \in [-\infty,1)}$ of reverse map projection embeddings, each one defining a unique new method of encoding classical data into quantum states. Inspired by well-known map projections from the unit sphere onto its tangent planes, used in practice in cartography, these embeddings address the common drawback of the amplitude embedding method, wherein scalar multiples of data points are identified and information about the norm of data is lost. We show how reverse map projections can be utilised as equivariant embeddings for quantum machine learning. Using these methods, we can leverage symmetries in classical datasets to significantly strengthen performance on quantum machine learning tasks. Finally, we select four values of $\alpha$ with which to perform a simple classification task, taking $E_\alpha$ as the embedding and experimenting with both equivariant and non-equivariant setups. We compare their results alongside those of standard amplitude embedding.
Quantum machine learning is in a period of rapid development and discovery, however it still lacks the resources and diversity of computational models of its classical complement. With the growing difficulties of classical models requiring extreme hardware and power solutions, and quantum models being limited by noisy intermediate-scale quantum (NISQ) hardware, there is an emerging opportunity to solve both problems together. Here we introduce a new software model for quantum neuromorphic computing -- a quantum leaky integrate-and-fire (QLIF) neuron, implemented as a compact high-fidelity quantum circuit, requiring only 2 rotation gates and no CNOT gates. We use these neurons as building blocks in the construction of a quantum spiking neural network (QSNN), and a quantum spiking convolutional neural network (QSCNN), as the first of their kind. We apply these models to the MNIST, Fashion-MNIST, and KMNIST datasets for a full comparison with other classical and quantum models. We find that the proposed models perform competitively, with comparative accuracy, with efficient scaling and fast computation in classical simulation as well as on quantum devices.
Variational quantum algorithms, optimized using gradient-based methods, often exhibit sub-optimal convergence performance due to their dependence on Euclidean geometry. Quantum natural gradient descent (QNGD) is a more efficient method that incorporates the geometry of the state space via a quantum information metric. However, QNGD is computationally intensive and suffers from high sample complexity. In this work, we formulate a novel quantum information metric and construct an unbiased estimator for this metric using single-shot measurements. We develop a quantum optimization algorithm that leverages the geometry of the state space via this estimator while avoiding full-state tomography, as in conventional techniques. We provide the convergence analysis of the algorithm under mild conditions. Furthermore, we provide experimental results that demonstrate the better sample complexity and faster convergence of our algorithm compared to the state-of-the-art approaches. Our results illustrate the algorithm's ability to avoid saddle points and local minima.
In the present study, we use cross-domain classification using quantum machine learning for quantum advantages to readdress the entanglement versus separability paradigm. The inherent structure of quantum states and its relation to a particular class of quantum states are used to intuitively classify testing states from domains different from training states, called \textit{cross-domain classification}. Using our quantum machine learning algorithm, we demonstrate efficient classifications of two-qubit mixed states into entangled and separable classes. For analyzing the quantumness of correlations, our model adequately classifies Bell diagonal states as zero and non-zero discord states. In addition, we also extend our analysis to evaluate the robustness of our model using random local unitary transformations. Our results demonstrate the potential of the quantum support vector machine for classifying quantum states across the multi-dimensional Hilbert space in comparison to classical support vector machines and neural networks.
In recent years, with the development of quantum machine learning, quantum neural networks (QNNs) have gained increasing attention in the field of natural language processing (NLP) and have achieved a series of promising results. However, most existing QNN models focus on the architectures of quantum recurrent neural network (QRNN) and self-attention mechanism (QSAM). In this work, we propose a novel QNN model based on quantum convolution. We develop the quantum depthwise convolution that significantly reduces the number of parameters and lowers computational complexity. We also introduce the multi-scale feature fusion mechanism to enhance model performance by integrating word-level and sentence-level features. Additionally, we propose the quantum word embedding and quantum sentence embedding, which provide embedding vectors more efficiently. Through experiments on two benchmark text classification datasets, we demonstrate our model outperforms a wide range of state-of-the-art QNN models. Notably, our model achieves a new state-of-the-art test accuracy of 96.77% on the RP dataset. We also show the advantages of our quantum model over its classical counterparts in its ability to improve test accuracy using fewer parameters. Finally, an ablation test confirms the effectiveness of the multi-scale feature fusion mechanism and quantum depthwise convolution in enhancing model performance.
Many Machine Learning (ML) models are referred to as black box models, providing no real insights into why a prediction is made. Feature importance and explainability are important for increasing transparency and trust in ML models, particularly in settings such as healthcare and finance. With quantum computing's unique capabilities, such as leveraging quantum mechanical phenomena like superposition, which can be combined with ML techniques to create the field of Quantum Machine Learning (QML), and such techniques may be applied to QML models. This article explores feature importance and explainability insights in QML compared to Classical ML models. Utilizing the widely recognized Iris dataset, classical ML algorithms such as SVM and Random Forests, are compared against hybrid quantum counterparts, implemented via IBM's Qiskit platform: the Variational Quantum Classifier (VQC) and Quantum Support Vector Classifier (QSVC). This article aims to provide a comparison of the insights generated in ML by employing permutation and leave one out feature importance methods, alongside ALE (Accumulated Local Effects) and SHAP (SHapley Additive exPlanations) explainers.
Quantum machine learning (QML) has the potential for improving the multi-label classification of rare, albeit critical, diseases in large-scale chest x-ray (CXR) datasets due to theoretical quantum advantages over classical machine learning (CML) in sample efficiency and generalizability. While prior literature has explored QML with CXRs, it has focused on binary classification tasks with small datasets due to limited access to quantum hardware and computationally expensive simulations. To that end, we implemented a Jax-based framework that enables the simulation of medium-sized qubit architectures with significant improvements in wall-clock time over current software offerings. We evaluated the performance of our Jax-based framework in terms of efficiency and performance for hybrid quantum transfer learning for long-tailed classification across 8, 14, and 19 disease labels using large-scale CXR datasets. The Jax-based framework resulted in up to a 58% and 95% speed-up compared to PyTorch and TensorFlow implementations, respectively. However, compared to CML, QML demonstrated slower convergence and an average AUROC of 0.70, 0.73, and 0.74 for the classification of 8, 14, and 19 CXR disease labels. In comparison, the CML models had an average AUROC of 0.77, 0.78, and 0.80 respectively. In conclusion, our work presents an accessible implementation of hybrid quantum transfer learning for long-tailed CXR classification with a computationally efficient Jax-based framework.
Quantum Machine Learning investigates the possibility of quantum computers enhancing Machine Learning algorithms. Anomaly segmentation is a fundamental task in various domains to identify irregularities at sample level and can be addressed with both supervised and unsupervised methods. Autoencoders are commonly used in unsupervised tasks, where models are trained to reconstruct normal instances efficiently, allowing anomaly identification through high reconstruction errors. While quantum autoencoders have been proposed in the literature, their application to anomaly segmentation tasks remains unexplored. In this paper, we introduce a patch-based quantum autoencoder (QPB-AE) for image anomaly segmentation, with a number of parameters scaling logarithmically with patch size. QPB-AE reconstructs the quantum state of the embedded input patches, computing an anomaly map directly from measurement through a SWAP test without reconstructing the input image. We evaluate its performance across multiple datasets and parameter configurations and compare it against a classical counterpart.
The study of variational quantum algorithms (VQCs) has received significant attention from the quantum computing community in recent years. These hybrid algorithms, utilizing both classical and quantum components, are well-suited for noisy intermediate-scale quantum devices. Though estimating exact gradients using the parameter-shift rule to optimize the VQCs is realizable in NISQ devices, they do not scale well for larger problem sizes. The computational complexity, in terms of the number of circuit evaluations required for gradient estimation by the parameter-shift rule, scales linearly with the number of parameters in VQCs. On the other hand, techniques that approximate the gradients of the VQCs, such as the simultaneous perturbation stochastic approximation (SPSA), do not scale with the number of parameters but struggle with instability and often attain suboptimal solutions. In this work, we introduce a novel gradient estimation approach called Guided-SPSA, which meaningfully combines the parameter-shift rule and SPSA-based gradient approximation. The Guided-SPSA results in a 15% to 25% reduction in the number of circuit evaluations required during training for a similar or better optimality of the solution found compared to the parameter-shift rule. The Guided-SPSA outperforms standard SPSA in all scenarios and outperforms the parameter-shift rule in scenarios such as suboptimal initialization of the parameters. We demonstrate numerically the performance of Guided-SPSA on different paradigms of quantum machine learning, such as regression, classification, and reinforcement learning.
The increasing capabilities of Machine Learning (ML) models go hand in hand with an immense amount of data and computational power required for training. Therefore, training is usually outsourced into HPC facilities, where we have started to experience limits in scaling conventional HPC hardware, as theorized by Moore's law. Despite heavy parallelization and optimization efforts, current state-of-the-art ML models require weeks for training, which is associated with an enormous $CO_2$ footprint. Quantum Computing, and specifically Quantum Machine Learning (QML), can offer significant theoretical speed-ups and enhanced expressive power. However, training QML models requires tuning various hyperparameters, which is a nontrivial task and suboptimal choices can highly affect the trainability and performance of the models. In this study, we identify the most impactful hyperparameters and collect data about the performance of QML models. We compare different configurations and provide researchers with performance data and concrete suggestions for hyperparameter selection.
Benchmarking models via classical simulations is one of the main ways to judge ideas in quantum machine learning before noise-free hardware is available. However, the huge impact of the experimental design on the results, the small scales within reach today, as well as narratives influenced by the commercialisation of quantum technologies make it difficult to gain robust insights. To facilitate better decision-making we develop an open-source package based on the PennyLane software framework and use it to conduct a large-scale study that systematically tests 12 popular quantum machine learning models on 6 binary classification tasks used to create 160 individual datasets. We find that overall, out-of-the-box classical machine learning models outperform the quantum classifiers. Moreover, removing entanglement from a quantum model often results in as good or better performance, suggesting that "quantumness" may not be the crucial ingredient for the small learning tasks considered here. Our benchmarks also unlock investigations beyond simplistic leaderboard comparisons, and we identify five important questions for quantum model design that follow from our results.
Machine learning, particularly deep neural networks, has been widely used in high-energy physics, demonstrating remarkable results in various applications. Furthermore, the extension of machine learning to quantum computers has given rise to the emerging field of quantum machine learning. In this paper, we propose the Quantum Complete Graph Neural Network (QCGNN), which is a variational quantum algorithm based model designed for learning on complete graphs. QCGNN with deep parametrized operators offers a polynomial speedup over its classical and quantum counterparts, leveraging the property of quantum parallelism. We investigate the application of QCGNN with the challenging task of jet discrimination, where the jets are represented as complete graphs. Additionally, we conduct a comparative analysis with classical models to establish a performance benchmark.