Machine learning and quantum computing are being progressively explored to shed light on possible computational approaches to deal with hitherto unsolvable problems. Classical methods for machine learning are ubiquitous in pattern recognition, with support vector machines (SVMs) being a prominent technique for network classification. However, there are limitations to the successful resolution of such classification instances when the input feature space becomes large, and the successive evaluation of so-called kernel functions becomes computationally exorbitant. The use of principal component analysis (PCA) substantially minimizes the dimensionality of feature space thereby enabling computational speed-ups of supervised learning: the creation of a classifier. Further, the application of quantum-based learning to the PCA reduced input feature space might offer an exponential speedup with fewer parameters. The present learning model is evaluated on a real clinical application: the diagnosis of Progressive Supranuclear Palsy (PSP) disorder. The results suggest that quantum machine learning has led to noticeable advancement and outperforms classical frameworks. The optimized variational quantum classifier classifies the PSP dataset with 86% accuracy as compared to conventional SVM. The other technique, a quantum kernel estimator, approximates the kernel function on the quantum machine and optimizes a classical SVM. In particular, we have demonstrated the successful application of the present model on both a quantum simulator and real chips of the IBM quantum platform.
Quantum machine learning (QML) investigates how quantum phenomena can be exploited in order to learn data in an alternative way, \textit{e.g.} by means of a quantum computer. While recent results evidence that QML models can potentially surpass their classical counterparts' performance in specific tasks, quantum technology hardware is still unready to reach quantum advantage in tasks of significant relevance to the broad scope of the computer science community. Recent advances indicate that hybrid classical-quantum models can readily attain competitive performances at low architecture complexities. Such investigations are often carried out for image-processing tasks, and are notably constrained to modelling \textit{raster images}, represented as a grid of two-dimensional pixels. Here, we introduce vector-based representation of sketch drawings as a test-bed for QML models. Such a lower-dimensional data structure results handful to benchmark model's performance, particularly in current transition times, where classical simulations of quantum circuits are naturally limited in the number of qubits, and quantum hardware is not readily available to perform large-scale experiments. We report some encouraging results for primitive hybrid classical-quantum architectures, in a canonical sketch recognition problem.
Quantum machine learning models based on parametrized quantum circuits, also called quantum neural networks (QNNs), are considered to be among the most promising candidates for applications on near-term quantum devices. Here we explore the expressivity and inductive bias of QNNs by exploiting an exact mapping from QNNs with inputs $x$ to classical perceptrons acting on $x \otimes x$ (generalised to complex inputs). The simplicity of the perceptron architecture allows us to provide clear examples of the shortcomings of current QNN models, and the many barriers they face to becoming useful general-purpose learning algorithms. For example, a QNN with amplitude encoding cannot express the Boolean parity function for $n\geq 3$, which is but one of an exponential number of data structures that such a QNN is unable to express. Mapping a QNN to a classical perceptron simplifies training, allowing us to systematically study the inductive biases of other, more expressive embeddings on Boolean data. Several popular embeddings primarily produce an inductive bias towards functions with low class balance, reducing their generalisation performance compared to deep neural network architectures which exhibit much richer inductive biases. We explore two alternate strategies that move beyond standard QNNs. In the first, we use a QNN to help generate a classical DNN-inspired kernel. In the second we draw an analogy to the hierarchical structure of deep neural networks and construct a layered non-linear QNN that is provably fully expressive on Boolean data, while also exhibiting a richer inductive bias than simple QNNs. Finally, we discuss characteristics of the QNN literature that may obscure how hard it is to achieve quantum advantage over deep learning algorithms on classical data.
This study investigates the potential of quantum machine learning to improve flood forecasting we focus on daily flood events along Germany's Wupper River in 2023 our approach combines classical machine learning techniques with QML techniques this hybrid model leverages quantum properties like superposition and entanglement to achieve better accuracy and efficiency classical and QML models are compared based on training time accuracy and scalability results show that QML models offer competitive training times and improved prediction accuracy this research signifies a step towards utilizing quantum technologies for climate change adaptation we emphasize collaboration and continuous innovation to implement this model in real-world flood management ultimately enhancing global resilience against floods
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.
Quantum machine learning (QML) requires significant quantum resources to address practical real-world problems. When the underlying quantum information exhibits hierarchical structures in the data, limitations persist in training complexity and generalization. Research should prioritize both the efficient design of quantum architectures and the development of learning strategies to optimize resource usage. We propose a framework called quantum curriculum learning (Q-CurL) for quantum data, where the curriculum introduces simpler tasks or data to the learning model before progressing to more challenging ones. Q-CurL exhibits robustness to noise and data limitations, which is particularly relevant for current and near-term noisy intermediate-scale quantum devices. We achieve this through a curriculum design based on quantum data density ratios and a dynamic learning schedule that prioritizes the most informative quantum data. Empirical evidence shows that Q-CurL significantly enhances training convergence and generalization for unitary learning and improves the robustness of quantum phase recognition tasks. Q-CurL is effective with broad physical learning applications in condensed matter physics and quantum chemistry.
Quantum machine learning (QML) is a rapidly expanding field that merges the principles of quantum computing with the techniques of machine learning. One of the powerful mathematical frameworks in this domain is tensor networks. These networks are used to approximate high-order tensors by contracting tensors with lower ranks. Initially developed for simulating quantum systems, tensor networks have become integral to quantum computing and, by extension, to QML. Drawing inspiration from these quantum methods, specifically the Matrix Product States (MPS), we apply them in a classical machine learning setting. Their ability to efficiently represent and manipulate complex, high-dimensional data makes them effective in a supervised learning framework. Here, we present an MPS model, in which the MPS functions as both a classifier and a generator. The dual functionality of this novel MPS model permits a strategy that enhances the traditional training of supervised MPS models. This framework is inspired by generative adversarial networks and is geared towards generating more realistic samples by reducing outliers. In addition, our contributions offer insights into the mechanics of tensor network methods for generation tasks. Specifically, we discuss alternative embedding functions and a new sampling method from non-normalized MPSs.
At the intersection of quantum computing and machine learning, this review paper explores the transformative impact these technologies are having on the capabilities of data processing and analysis, far surpassing the bounds of traditional computational methods. Drawing upon an in-depth analysis of 32 seminal papers, this review delves into the interplay between quantum computing and machine learning, focusing on transcending the limitations of classical computing in advanced data processing and applications. This review emphasizes the potential of quantum-enhanced methods in enhancing cybersecurity, a critical sector that stands to benefit significantly from these advancements. The literature review, primarily leveraging Science Direct as an academic database, delves into the transformative effects of quantum technologies on machine learning, drawing insights from a diverse collection of studies and scholarly articles. While the focus is primarily on the growing significance of quantum computing in cybersecurity, the review also acknowledges the promising implications for other sectors as the field matures. Our systematic approach categorizes sources based on quantum machine learning algorithms, applications, challenges, and potential future developments, uncovering that quantum computing is increasingly being implemented in practical machine learning scenarios. The review highlights advancements in quantum-enhanced machine learning algorithms and their potential applications in sectors such as cybersecurity, emphasizing the need for industry-specific solutions while considering ethical and security concerns. By presenting an overview of the current state and projecting future directions, the paper sets a foundation for ongoing research and strategic advancement in quantum machine learning.
The quest for successful variational quantum machine learning (QML) relies on the design of suitable parametrized quantum circuits (PQCs), as analogues to neural networks in classical machine learning. Successful QML models must fulfill the properties of trainability and non-dequantization, among others. Recent works have highlighted an intricate interplay between trainability and dequantization of such models, which is still unresolved. In this work we contribute to this debate from the perspective of machine learning, proving a number of results identifying, among others when trainability and non-dequantization are not mutually exclusive. We begin by providing a number of new somewhat broader definitions of the relevant concepts, compared to what is found in other literature, which are operationally motivated, and consistent with prior art. With these precise definitions given and motivated, we then study the relation between trainability and dequantization of variational QML. Next, we also discuss the degrees of "variationalness" of QML models, where we distinguish between models like the hardware efficient ansatz and quantum kernel methods. Finally, we introduce recipes for building PQC-based QML models which are both trainable and nondequantizable, and corresponding to different degrees of variationalness. We do not address the practical utility for such models. Our work however does point toward a way forward for finding more general constructions, for which finding applications may become feasible.
Quantum machine learning models use encoding circuits to map data into a quantum Hilbert space. While it is well known that the architecture of these circuits significantly influences core properties of the resulting model, they are often chosen heuristically. In this work, we present a novel approach using reinforcement learning techniques to generate problem-specific encoding circuits to improve the performance of quantum machine learning models. By specifically using a model-based reinforcement learning algorithm, we reduce the number of necessary circuit evaluations during the search, providing a sample-efficient framework. In contrast to previous search algorithms, our method uses a layered circuit structure that significantly reduces the search space. Additionally, our approach can account for multiple objectives such as solution quality, hardware restrictions and circuit depth. We benchmark our tailored circuits against various reference models, including models with problem-agnostic circuits and classical models. Our results highlight the effectiveness of problem-specific encoding circuits in enhancing QML model performance.
Quantum machine learning has demonstrated significant potential in solving practical problems, particularly in statistics-focused areas such as data science and finance. However, challenges remain in preparing and learning statistical models on a quantum processor due to issues with trainability and interpretability. In this letter, we utilize the maximum entropy principle to design a statistics-informed parameterized quantum circuit (SI-PQC) for efficiently preparing and training of quantum computational statistical models, including arbitrary distributions and their weighted mixtures. The SI-PQC features a static structure with trainable parameters, enabling in-depth optimized circuit compilation, exponential reductions in resource and time consumption, and improved trainability and interpretability for learning quantum states and classical model parameters simultaneously. As an efficient subroutine for preparing and learning in various quantum algorithms, the SI-PQC addresses the input bottleneck and facilitates the injection of prior knowledge.
Although quantum machine learning has been introduced for a while, its applications in computer vision are still limited. This paper, therefore, revisits the quantum visual encoding strategies, the initial step in quantum machine learning. Investigating the root cause, we uncover that the existing quantum encoding design fails to ensure information preservation of the visual features after the encoding process, thus complicating the learning process of the quantum machine learning models. In particular, the problem, termed "Quantum Information Gap" (QIG), leads to a gap of information between classical and corresponding quantum features. We provide theoretical proof and practical demonstrations of that found and underscore the significance of QIG, as it directly impacts the performance of quantum machine learning algorithms. To tackle this challenge, we introduce a simple but efficient new loss function named Quantum Information Preserving (QIP) to minimize this gap, resulting in enhanced performance of quantum machine learning algorithms. Extensive experiments validate the effectiveness of our approach, showcasing superior performance compared to current methodologies and consistently achieving state-of-the-art results in quantum modeling.
Quantum machine learning (QML) requires powerful, flexible and efficiently trainable models to be successful in solving challenging problems. We introduce density quantum neural networks, a model family that prepares mixtures of trainable unitaries, with a distributional constraint over coefficients. This framework balances expressivity and efficient trainability, especially on quantum hardware. For expressivity, the Hastings-Campbell Mixing lemma converts benefits from linear combination of unitaries into density models with similar performance guarantees but shallower circuits. For trainability, commuting-generator circuits enable density model construction with efficiently extractable gradients. The framework connects to various facets of QML including post-variational and measurement-based learning. In classical settings, density models naturally integrate the mixture of experts formalism, and offer natural overfitting mitigation. The framework is versatile - we uplift several quantum models into density versions to improve model performance, or trainability, or both. These include Hamming weight-preserving and equivariant models, among others. Extensive numerical experiments validate our findings.
Graph Neural Networks (GNNs) are powerful machine learning models that excel at analyzing structured data represented as graphs, demonstrating remarkable performance in applications like social network analysis and recommendation systems. However, classical GNNs face scalability challenges when dealing with large-scale graphs. This paper proposes frameworks for implementing GNNs on quantum computers to potentially address the challenges. We devise quantum algorithms corresponding to the three fundamental types of classical GNNs: Graph Convolutional Networks, Graph Attention Networks, and Message-Passing GNNs. A complexity analysis of our quantum implementation of the Simplified Graph Convolutional (SGC) Network shows potential quantum advantages over its classical counterpart, with significant improvements in time and space complexities. Our complexities can have trade-offs between the two: when optimizing for minimal circuit depth, our quantum SGC achieves logarithmic time complexity in the input sizes (albeit at the cost of linear space complexity). When optimizing for minimal qubit usage, the quantum SGC exhibits space complexity logarithmic in the input sizes, offering an exponential reduction compared to classical SGCs, while still maintaining better time complexity. These results suggest our Quantum GNN frameworks could efficiently process large-scale graphs. This work paves the way for implementing more advanced Graph Neural Network models on quantum computers, opening new possibilities in quantum machine learning for analyzing graph-structured data.
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.
Despite their ever more widespread deployment throughout society, machine learning algorithms remain critically vulnerable to being spoofed by subtle adversarial tampering with their input data. The prospect of near-term quantum computers being capable of running {quantum machine learning} (QML) algorithms has therefore generated intense interest in their adversarial vulnerability. Here we show that quantum properties of QML algorithms can confer fundamental protections against such attacks, in certain scenarios guaranteeing robustness against classically-armed adversaries. We leverage tools from many-body physics to identify the quantum sources of this protection. Our results offer a theoretical underpinning of recent evidence which suggest quantum advantages in the search for adversarial robustness. In particular, we prove that quantum classifiers are: (i) protected against weak perturbations of data drawn from the trained distribution, (ii) protected against local attacks if they are insufficiently scrambling, and (iii) protected against universal adversarial attacks if they are sufficiently quantum chaotic. Our analytic results are supported by numerical evidence demonstrating the applicability of our theorems and the resulting robustness of a quantum classifier in practice. This line of inquiry constitutes a concrete pathway to advantage in QML, orthogonal to the usually sought improvements in model speed or accuracy.
In this paper, we explore the power of Quantum Machine Learning as we extend, implement and evaluate algorithms like Quantum Support Vector Classifier (QSVC), Pegasos-QSVC, Variational Quantum Circuits (VQC), and Quantum Neural Networks (QNN) in Qiskit with diverse feature mapping techniques for genomic sequence classification.
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.
Parameterized quantum circuits (PQCs) are fundamental to quantum machine learning (QML), quantum optimization, and variational quantum algorithms (VQAs). The expressibility of PQCs is a measure that determines their capability to harness the full potential of the quantum state space. It is thus a crucial guidepost to know when selecting a particular PQC ansatz. However, the existing technique for expressibility computation through statistical estimation requires a large number of samples, which poses significant challenges due to time and computational resource constraints. This paper introduces a novel approach for expressibility estimation of PQCs using Graph Neural Networks (GNNs). We demonstrate the predictive power of our GNN model with a dataset consisting of 25,000 samples from the noiseless IBM QASM Simulator and 12,000 samples from three distinct noisy quantum backends. The model accurately estimates expressibility, with root mean square errors (RMSE) of 0.05 and 0.06 for the noiseless and noisy backends, respectively. We compare our model's predictions with reference circuits [Sim and others, QuTe'2019] and IBM Qiskit's hardware-efficient ansatz sets to further evaluate our model's performance. Our experimental evaluation in noiseless and noisy scenarios reveals a close alignment with ground truth expressibility values, highlighting the model's efficacy. Moreover, our model exhibits promising extrapolation capabilities, predicting expressibility values with low RMSE for out-of-range qubit circuits trained solely on only up to 5-qubit circuit sets. This work thus provides a reliable means of efficiently evaluating the expressibility of diverse PQCs on noiseless simulators and hardware.
Ensuring data privacy in machine learning models is critical, particularly in distributed settings where model gradients are typically shared among multiple parties to allow collaborative learning. Motivated by the increasing success of recovering input data from the gradients of classical models, this study addresses a central question: How hard is it to recover the input data from the gradients of quantum machine learning models? Focusing on variational quantum circuits (VQC) as learning models, we uncover the crucial role played by the dynamical Lie algebra (DLA) of the VQC ansatz in determining privacy vulnerabilities. While the DLA has previously been linked to the classical simulatability and trainability of VQC models, this work, for the first time, establishes its connection to the privacy of VQC models. In particular, we show that properties conducive to the trainability of VQCs, such as a polynomial-sized DLA, also facilitate the extraction of detailed snapshots of the input. We term this a weak privacy breach, as the snapshots enable training VQC models for distinct learning tasks without direct access to the original input. Further, we investigate the conditions for a strong privacy breach where the original input data can be recovered from these snapshots by classical or quantum-assisted polynomial time methods. We establish conditions on the encoding map such as classical simulatability, overlap with DLA basis, and its Fourier frequency characteristics that enable such a privacy breach of VQC models. Our findings thus play a crucial role in detailing the prospects of quantum privacy advantage by guiding the requirements for designing quantum machine learning models that balance trainability with robust privacy protection.