How Many Qubits Does a Machine Learning Problem Require?

In this work, we studied the use of Quantum Machine Learning (QML) algorithms for binary classification and compared their performance with classical Machine Learning (ML) methods. QML merges principles of Quantum Computing (QC) and ML, offering improved efficiency and potential quantum advantage in data-driven tasks and when solving complex problems. In binary classification, where the goal is to assign data to one of two categories, QML uses quantum algorithms to process large datasets efficiently. Quantum algorithms like Quantum Support Vector Machines (QSVM) and Quantum Neural Networks (QNN) exploit quantum parallelism and entanglement to enhance performance over classical methods. This study focuses on two common QML algorithms, Quantum Support Vector Classifier (QSVC) and QNN. We used the Qiskit software and conducted the experiments with three different datasets. Data preprocessing included dimensionality reduction using Principal Component Analysis (PCA) and standardization using scalers. The results showed that quantum algorithms demonstrated competitive performance against their classical counterparts in terms of accuracy, while QSVC performed better than QNN. These findings suggest that QML holds potential for improving computational efficiency in binary classification tasks. This opens the way for more efficient and scalable solutions in complex classification challenges and shows the complementary role of quantum computing.

Advances in Quantum Machine Learning and Deep Learning for Image Classification: A Survey

Quantum kernel methods have been widely recognized as one of the promising quantum machine learning (QML) algorithms that have the potential to achieve quantum advantages. However, their capabilities may be severely degraded by inevitable noises in the current noisy intermediate-scale quantum (NISQ) era. In this article, we theoretically characterize the power of noisy quantum kernels and demonstrate that under depolarizing noise, quantum kernel methods may only have very poor prediction capability, even when the generalization error is small. Specifically, we quantitatively describe the decreasing of the prediction capability of noisy quantum kernels in terms of the rate of quantum noise, the size of training samples, the number of qubits, and the number of layers affected by quantum noises. Our results clearly demonstrate that for a given number of training samples, once the number of layers affected by noise exceeds some threshold, the prediction capability of noisy kernels is very poor. Thus, we provide a crucial warning to employ noisy quantum kernel methods for quantum computation and the theoretical results can also serve as guidelines when developing practical quantum kernel algorithms for achieving quantum advantages.

We have developed two quantum classifier models for the ttH classification problem, both of which fall into the category of hybrid quantumclassical algorithms for Noisy Intermediate Scale Quantum devices (NISQ). Our results, along with other studies, serve as a proof of concept that Quantum Machine Learning (QML) methods can have similar or better performance, in specific cases of low number of training samples, with respect to conventional ML methods even with a limited number of qubits available in current hardware. To utilise algorithms with a low number of qubits — to accommodate for limitations in both simulation hardware and real quantum hardware — we investigated different feature reduction methods. Their impact on the performance of both the classical and quantum models was assessed. We addressed different implementations of two QML models, representative of the two main approaches to supervised quantum machine learning today: a Quantum Support Vector Machine (QSVM), a kernel-based method, and a Variational Quantum Circuit (VQC), a variational approach.

Blood group classification is a critical aspect of medical diagnostics, essential for transfusion medicine, organ transplantation and prenatal care.Traditional serological methods while effective, are time-consuming, require specialized laboratory facilities and are subject to human error.This research introduces a novel quantum-enhanced approach to blood group classification that combines deep learning techniques with quantum machine learning algorithms.Our methodology leverages convolutional neural networks (CNNs) optimized through quantum computing principles to analyze blood sample images for accurate and rapid blood group determination.Using a comprehensive dataset of 10,000 blood sample images across eight blood groups (A+, A-, B+, B-, AB+, AB-, O+, O-), we developed and validated our hybrid quantum-classical model.The proposed quantum-enhanced CNN achieved 99.5% classification accuracy, outperforming traditional serological methods (95.0%) and conventional machine learning approaches such as SVM (97.5%) and Random Forest (98.0%).Processing time was significantly reduced from 300 seconds for traditional methods to just 3.5 seconds for our quantum-enhanced approach.We further evaluated various CNN architectures with ResNet50 demonstrating the highest accuracy (99.0%) among classical implementations.The quantum advantage was particularly evident with larger datasets, showing consistent performance improvements across all testing scenarios.Our approach addresses critical gaps in current blood typing methodologies by providing a non-invasive, rapid and highly accurate alternative that can be deployed in resource-limited settings and emergency situations.This research demonstrates the practical application of quantum computing principles in healthcare diagnostics and establishes a foundation for further exploration of quantum-enhanced medical image analysis [1][2][3] .

Even after decades of quantum computing development, examples of generally useful quantum algorithms with exponential speedups over classical counterparts are scarce. Recent progress in quantum algorithms for linear-algebra positioned quantum machine learning (QML) as a potential source of such useful exponential improvements. Yet, in an unexpected development, a recent series of "dequantization" results has equally rapidly removed the promise of exponential speedups for several QML algorithms. This raises the critical question whether exponential speedups of other linear-algebraic QML algorithms persist. In this paper, we study the quantum-algorithmic methods behind the algorithm for topological data analysis of Lloyd, Garnerone and Zanardi through this lens. We provide evidence that the problem solved by this algorithm is classically intractable by showing that its natural generalization is as hard as simulating the one clean qubit model – which is widely believed to require superpolynomial time on a classical computer – and is thus very likely immune to dequantizations. Based on this result, we provide a number of new quantum algorithms for problems such as rank estimation and complex network analysis, along with complexity-theoretic evidence for their classical intractability. Furthermore, we analyze the suitability of the proposed quantum algorithms for near-term implementations. Our results provide a number of useful applications for full-blown, and restricted quantum computers with a guaranteed exponential speedup over classical methods, recovering some of the potential for linear-algebraic QML to become one of quantum computing's killer applications.

This rapid growth in data and the increased complexity of machine learning models have made it almost impossible to continue pushing forward with classical computing, thereby creating a pressing need for new computational paradigms. The following paper will examine how quantum machine learning answers the above questions by applying the principles of quantum mechanics to the art of artificial intelligence (AI) and big data analytics. We examine some of the current Quantum Machine Learning (QML) algorithms and their applications based on a framework that employs quantum-enhanced feature spaces, variational quantum circuits, and quantum-inspired classical algorithms. Our methodology combines theoretical analysis with empirical evaluation of these methods over standard benchmark datasets, using both quantum simulators and real quantum hardware. Key findings include a set of advantages carried by QML in specific fields, such as dimensionality reduction, optimization problems, and some clustering tasks. These are the quadratic speedup for support vector machines and the exponential advantage for principal component analysis. Our results also show that quantum error correction isn’t perfect and that loading classical data into a quantum system can be hard. We conclude that, while QML holds much promise, it is, by all means, clearly still a way off from being considered a panacea. It is awaiting further breakthroughs in quantum hardware, error mitigation techniques, and algorithm design in order to fully realize its potential. This work thus presents a roadmap for future research and highlights where QML is best placed to make major impactful differences in artificial intelligence and big data analytics.

Variational quantum circuits (VQC) lie at the forefront of quantum machine learning research. Still, the use of quantum networks for real data processing remains challenging as the number of available qubits cannot accommodate a large dimensionality of data—if the usual angle encoding scenario is used. To achieve dimensionality reduction, Principal Component Analysis is routinely applied as a pre-processing method before the embedding of the classical features on qubits. In this work, we propose an alternative method which reduces the dimensionality of a given dataset by taking into account the specific quantum embedding that comes after. This method aspires to make quantum machine learning with VQCs more versatile and effective on datasets of high dimension. At a second step, we propose a quantum-inspired classical autoencoder model which can be used to encode information in low latent spaces. The power of our proposed models is exhibited via numerical tests. We show that our targeted dimensionality reduction method considerably boosts VQC’s performance, and we also identify cases for which the second model outperforms classical autoencoders in terms of reconstruction loss.

In recent years, Variational Quantum Circuit (VQC)s have been widely explored to advance quantum circuits against classic models on various domains, such as quantum chemistry and quantum machine learning. Similar to classic machine-learning models, VQCs can be optimized through gradient-based approaches. However, the gradient of VQCs may dramatically vanish during the optimization process as the number of qubits or layers increases. This issue, known as Barren Plateau (BP)s, seriously hinders the scaling of VQCs on large datasets. To mitigate the exponential gradient vanishing, extensive efforts have been devoted to tackling this issue through different methods. Some BP mitigation strategies include VQC parameter initialization and more complex VQC architectures such as Quantum Neural Network (QNN)s and Quantum Convolutional Neural Network (QCNN). In this thesis, we aim to investigate several circuit components through the lens of parameter initialization techniques. We study the performance and gradient variance of the different quantum circuit structures in combination with various initialization methods. In most existing studies, researchers typically focus on improving or understanding one aspect of the VQC approach. Instead, we plan to investigate how the two components of the VQC behave as we interchange the different variables of the circuit. This investigation will provide a better understanding of how the VQC structures behave under different initialization strategies for binary classification problems.

Quantum machine learning has emerged as a potential practical application of near-term quantum devices. In this work, we study a two-layer hybrid classical-quantum classifier in which a first layer of quantum stochastic neurons implementing generalized linear models (QGLMs) is followed by a second classical combining layer. The input to the first, hidden, layer is obtained via amplitude encoding in order to leverage the exponential size of the fan-in of the quantum neurons in the number of qubits per neuron. To facilitate implementation of the QGLMs, all weights and activations are binary. While the state of the art on training strategies for this class of models is limited to exhaustive search and single-neuron perceptron-like bit-flip strategies, this letter introduces a stochastic variational optimization approach that enables the joint training of quantum and classical layers via stochastic gradient descent. Experiments show the advantages of the approach for a variety of activation functions implemented by QGLM neurons.

Accurate prediction of molecular properties is crucial for accelerating the development of new drugs, and quantum machine learning (QML) holds great promise in this domain. A typical QML pipeline comprises two core stages: encoding classical data into quantum representations followed by training and prediction using quantum computing-based machine learning (ML) models. In this article, we focus on the initial encoding stage and propose an effective quantum feature extraction approach for molecular graph data, introducing quantum node embedding and quantum edge embedding methods. We developed a hybrid quantum-classical ML framework and implemented several quantum-embedded graph neural network (QEGNN) models to evaluate the proposed method. Experiments conducted on three benchmark data sets with diverse molecular property prediction tasks demonstrate that QEGNN models consistently achieve higher accuracy, improved stability, and significantly reduced parameter complexity─hallmarks of quantum advantage. Furthermore, we validate the reliability of the quantum embedding approach on the superconducting quantum processor "Wukong," showing that the models retain stable performance even under the constraints of current noisy quantum hardware. This work highlights the potential of QML and paves the way for the development of universal QML models.

Nowadays, quantum-enhanced methods have been widely studied to solve machine learning related problems. This article presents the application of a Variational Quantum Classifier (VQC) for binary classification. We utilized three datasets: a synthetic dataset with randomly generated values between 0 and 1, the publicly available University of California Intelligence Machine learning (UCI) sonar dataset consisting of mining data, and a proprietary diabetes dataset related to diabetes with acute diseases and diabetes without acute disease. To deal with the limitation of noisy intermediate-scale quantum systems (NISQ), we used a pre-processing method to enhance the prediction rate when applying the VQC method. The process includes feature selection and state preparation. Quantum state preparation is critical for obtaining a functioning pipeline in a quantum machine learning (QML) model. Amplitude encoding is a state preparation approach that enhances the performance of data encoding and the learning of quantum models. As a result, our proposed methods achieved accuracies of 75%, 71.4%, and 68.73% by using VQC model and in contrast, the amplitude encoding-based VQC achieved 98.40%, 67.3%, and 74.50% accuracies on the synthetic, sonar, and diabetes dataset, respectively.

The search for an application of near-term quantum devices is widespread. Quantum machine learning is touted as a potential utilisation of such devices, particularly those out of reach of the simulation capabilities of classical computers. In this work, we study such an application in generative modelling, focussing on a class of quantum circuits known as Born machines. Specifically, we define a subset of this class based on Ising Hamiltonians and show that the circuits encountered during gradient-based training cannot be efficiently sampled from classically up to multiplicative error in the worst case. Our gradient-based training methods use cost functions known as the Sinkhorn divergence and the Stein discrepancy, which have not previously been used in the gradient-based training of quantum circuits, and we also introduce quantum kernels to generative modelling. We show that these methods outperform the previous standard method, which used maximum mean discrepancy (MMD) as a cost function, and achieve this with minimal overhead. Finally, we discuss the ability of the model to learn hard distributions and provide formal definitions for ‘quantum learning supremacy’. We also exemplify the work of this paper by using generative modelling to perform quantum circuit compilation.

Quantum Machine Learning (QML) is an emerging, powerful paradigm at the intersection of quantum computing and artificial intelligence, with the potential to enhance medical image analysis. We compared their performance with classical counterparts, while critically examining the gap between theoretical quantum advantages and the practical constraints of current Noisy Intermediate-Scale Quantum (NISQ) implementations. This review explored the current landscape of QML-based methodologies applied to key medical imaging modalities - Magnetic Resonance Imaging (MRI), Computed Tomography (CT), X-rays, and histopathology. We systematically analyzed how quantum-enhanced models were employed for critical tasks such as image classification, segmentation, and reconstruction, and we compared their performance with that of classical counterparts. The review delved into the architectural innovations that enabled these quantum approaches, including hybrid quantum-classical frameworks, variational quantum circuits, and quantum convolutional neural networks. Particular emphasis was given to the clinical relevance of QML applications, from early diagnostics to real-time surgery planning, and how quantum advantage might influence data efficiency, interpretability, along computational scalability. Finally, we highlighted current challenges in data encoding, noise resilience, and hardware limitations, and discussed promising future directions that could enable the practical deployment of QML in healthcare settings. This comprehensive review aimed to serve as a foundational reference for researchers and practitioners looking to harness quantum computing in medical imaging and precision medicine.

A time-series prediction framework using sequential learning algorithms and dimensionality reduction within a sparsification approach