Abstract Deep neural networks have established themselves as one of the most promising machine learning techniques. Training such models at large scales is often parallelized, giving rise to the concept of distributed deep learning. Distributed techniques are often employed in training large models or large datasets either out of necessity or simply for speed. Quantum machine learning, on the other hand, is the interplay between machine learning and quantum computing. It seeks to understand the advantages of employing quantum devices in developing new learning algorithms as well as improving the existing ones. A set of architectures that are heavily explored in quantum machine learning are quantum neural networks. In this review, we consider ideas from distributed deep learning as they apply to quantum neural networks. We find that the distribution of quantum datasets shares more similarities with its classical counterpart than does the distribution of quantum models, though the unique aspects of quantum data introduce new vulnerabilities to both approaches. We review the current state of the art in distributed quantum neural networks, including recent numerical experiments and the concept ofcircuit-cutting.
Abstract Deep neural networks have established themselves as one of the most promising machine learning techniques. Training such models at large scales is often parallelized, giving rise to the concept of distributed deep learning. Distributed techniques are often employed in training large models or large datasets either out of necessity or simply for speed. Quantum machine learning, on the other hand, is the interplay between machine learning and quantum computing. It seeks to understand the advantages of employing quantum devices in developing new learning algorithms as well as improving the existing ones. A set of architectures that are heavily explored in quantum machine learning are quantum neural networks. In this review, we consider ideas from distributed deep learning as they apply to quantum neural networks. We find that the distribution of quantum datasets shares more similarities with its classical counterpart than does the distribution of quantum models, though the unique aspects of quantum data introduce new vulnerabilities to both approaches. We review the current state of the art in distributed quantum neural networks, including recent numerical experiments and the concept ofcircuit-cutting.
One of the most promising new directions in quantum computing and artificial intelligence convergence is the Quantum Neural Networks (QNNs) that can potentially revolutionize the manner in which intelligent systems are designed, trained, and implemented. Although traditional deep learning models have proven to be incredibly successful in fields like computer vision, natural language processing and autonomous systems, they are becoming limited by computational bottlenecks, energy use, and scalability constraints when operating on large high-dimensional data. The distinctive principles of quantum mechanics (superposition, entanglement, and quantum parallelism) may be applied to the QNNs to provide a distinct computational paradigm with the ability to execute exponentially complicated computations more effectively than his classical counterparts. This article gives an in-depth analysis of QNNs as the new frontier of artificial intelligence. We start with the description of the theoretical foundations of quantum computation and their realization in the form of neural networks. We then examine state-of-the-art QNN architectures, such as hybrid quantum-classical models that help overcome present quantum hardware limitations in relation to the capabilities of classical machine learning. Some of the upcoming applications are showcased including molecular simulation and drug discovery and financial modeling, optimization, cryptography and intelligent automation. Such applications reveal the revolutionary power of QNNs to tackle the issues that cannot be tackled by traditional systems. Nonetheless, there are also major obstacles on the way to a practical implementation of QNN. Problems that still remain a barrier to widespread adoption include quantum decoherence, noise in near-term quantum devices, and the inability to scale qubit architectures or to train large-scale quantum models. In order to overcome these obstacles, we speak about the current research work on the topic of error correction, variational algorithms, and hybrid system designs. Also we examine the ethical and societal ramifications of quantum-accelerated AI, such as security, data sovereignty, and technological equity globally.
Quantum computing has an enormous potential in machine learning, where problems can quickly scale to be intractable for classical computation. Quantum machine learning is research area that combines the interplay of ideas from quantum computing and machine learning. Powerful and useful machine learning is dependent on having large-scale datasets used to train the models to be able to solve real-life problems. Currently, quantum machine learning lacks a plethora of large-scale quantum datasets required to further develop the models and test the quantum machine learning algorithms. Lack of large datasets is currently limiting the quantum advantage in the field of quantum machine learning. In this thesis, the concept of quantum data and different types of applied quantum datasets used to develop quantum machine learning models is studied. The research methodology is based on a systematic and comparative literature review of the state of the art articles in quantum computing and quantum machine learning in the recent years. We classify datasets into inherent and non-inherent quantum data based on the nature of the data. The preliminary literature review addresses patterns in the applied quantum machine learning. Testing and benchmarking QML models primarily uses non-inherent quantum data, or classical data encoded into the quantum system, while separate research is focused on generating inherent quantum datasets.
Quantum machine learning is at the crossroads of two of the most exciting current areas of research: quantum computing and classical machine learning. Although the field is still in its infancy, the body of literature is already large enough to warrant several review articles [1–3]. This short survey focuses on a selection of significant recent results on the subtopic of quantum neural networks, an area that hopes to build on the enormous impact that classical neural networks have had. In particular, we concentrate on quantum generalizations of popular neural-network concepts such as Boltzmann machines, generative adversarial networks and autoencoders, as well as applications of classical neural networks to quantum information and vice versa. Examples of Boltzmann machines. In a fully connected Boltzmann machine, connections exist between all visible and hidden neurons. In a restricted Boltzmann machine (RBM), there are no connections between neurons of the same type. A deep Boltzmann machine (DBM) consists of adding one or more additional layers of hidden neurons to an RBM, with no connections between neurons in the same layer. The energy-based nature of BMs gives a natural framework for considering quantum generalizations of their behavior. The BM energy function is equivalent to the Hamiltonian of a simple Ising model and one might hope that more general Hamiltonians allowed by quantum mechanics could explain certain data sets better than classically. Amin et al. [4] adopt this approach, and take the so-called transverse field Ising Hamiltonian as the energy function. This increased generality brings certain difficulties, however, as the transverse field term makes training the quantum Boltzmann machine (QBM) non-trivial. Although the general scaling and performance of QBMs is not yet well understood, for certain small-size examples the authors observe that their QBMs can learn data distributions better than classical BMs. Kieferova and Wiebe [5] extend the formalism of Amin et al. and consider more general Hamiltonians that, unlike the transverse Ising model, are not in general believed to be classically efficiently simulatable. Furthermore, they propose new methods for training that allow for parameters corresponding to quantum terms to be learned. Finally, their QBM enables a form of quantum-state tomography that can learn non-classical data, and also generate copies of the reconstructed state. Again, small-scale numerical evidence suggests that their proposals may provide an advantage over classical BMs, although their tendency to overfit data must be investigated further. The practical value of BMs, either classical or quantum, relies in part on the ease with which they are trained. This in turn depends on sampling efficiently from the Boltzmann distribution. Classically this can be done approximately only for the special case of restricted Boltzmann machines (RBM), i.e. where connections are between visible and hidden units, and no connections exist between neurons of the same type. Wiebe et al. [6] propose two quantum algorithms for Boltzmann sampling, based on starting from a state corresponding to the product distribution that is closest to the target Boltzmann distribution. While small-scale numerical studies are encouraging, true bounds on the running time of their algorithms rely on a problem-dependent parameter κ, the scaling of which is hard to estimate. The hope remains though that empirically their algorithms work well in practice, even for multi-layer and fully connected BMs. The expressive power of BMs for compactly representing complicated probability distributions has led to another line of investigation, namely their use for representing quantum many-body wave functions. The authors apply this technique to two prototypical spin models and achieve high accuracy in both ground-state estimation and dynamical evolution, improving on existing state-of-the-art techniques. Their results indicate that RBM states can capture complex many-body correlations in an efficient manner—evidence reinforced by the work of Deng et al. [8], who show that certain topological quantum states in one, two and three dimensions can be represented by RBM states with a number of parameters only linear in the system size. In a subsequent study, however, Gao and Duan [9] prove that although RBM states can indeed represent many highly entangled states, their expressive power is limited in that they cannot represent arbitrary states generated by polynomial-sized quantum circuits, nor those that are the ground states of k-local Hamiltonians with polynomial-sized energy gaps, unless the polynomial hierarchy from computational complexity theory collapses. On the other hand, they show that these two important classes of states can be efficiently represented by a deep Boltzmann machine of three layers. Intriguingly though, another paper by Deng et al. [10] gives an analytic construction of a family of RBM states with a number of parameters linear in the system size that exhibits maximal volume-law entanglement, and that cannot be represented efficiently by either matrix product states (MPS) or tensor-network (TN) states. This shows that the expressive power of even efficiently parametrized RBM states is not limited by entanglement in the same way that other popular compact representations are. This gives the hope that RBM states may prove a valuable tool in understanding entangled quantum systems intractable by traditional methods. Levine et al. [11] establish another connection between the many-body wave function and neural networks, this time in the form of convolutional arithmetic circuits (ConvAC), a variant of the popular convolutional neural networks in widespread use today. By proving a one-to-one equivalence between a ConvAC circuit and TN quantum states, the authors are able to use tools from quantum information theory to analyze the entanglement present in the corresponding TN, and quantify the neural network's ability to model complex correlations between its inputs. This in turn can be used to obtain bounds on the expressivity of a given ConvAC architecture and be of practical use in choosing network parameters tailored to the data. While ConvAC are not widely used in practice, the authors empirically validate that the insights gained can be applied successfully to more common convolutional neural-network designs. Generative adversarial networks (GAN) are machine-learning algorithms in which two players—a generator and a discriminator—compete against each another. The generator's goal is to create and send fake data samples to the discriminator and maximize the probability that the discriminator erroneously believes that the sample comes from some true data distribution. The discriminator attempts to discern real from fake data as best as possible. Under reasonable assumptions the game converges to a point where the discriminator is unable to discriminate with probability greater than 1/2 (i.e. no better than random guessing), and the generator in fact has learned to generate data from the true distribution. Lloyd and Weedbrook [12] consider the natural extension in which one or both of the generator and discriminator are equipped with quantum information processors. When the data to be learned are a quantum state and both parties have quantum processors, the authors show that the unique end point of the adversarial game also coincides with the generator producing a quantum state corresponding to the true data statistics, and the discriminator unable to discern true from false data better than random guessing. They further argue that a different outcome may hold when the true samples are produced by the measurement of some quantum state, and the generator is purely classical. The concept of quantum supremacy is based on the assumption that there exist probability distributions accessible to a quantum computer that no classical computer can efficiently sample from. If the true data correspond to one of these distributions, then no classical generator can efficiently generate fake data reproducing the true statistics and, in principle, the discriminator can successfully discriminate true from fake data. However, whether the discriminator can efficiently find the measurements required to do so is unclear. Quantum-computing techniques have also found applications in autoencoders—neural networks where a larger number of input and output neurons are connected via a smaller number of intermediary latent neurons. The goal is to tune the weights of the network so that a training set of classical bit strings can be approximately recovered after being passed through the autoencoder. Romero et al. [13] consider instead a training set of quantum states, and ask whether a quantum circuit with a similar bottleneck structure can compress and approximately recover the data. The circuits that they consider consist of gates chosen from some set of parametrized unitary operations, and arranged in some fixed order. The parameters are then optimized classically so that the circuit best predicts the training-set labels. The authors demonstrate the validity of this approach by showing that ground states of the Hubbard model and certain molecules can indeed be compressed and recovered by such circuits. However, in general, the performance of such quantum autoencoders will be highly dependent on the kind of programmable circuit on which they are based, and at present there does not seem to be a structured way of determining this. Quantum neural networks are still in their infancy and, while the above works are important steps towards bridging our understanding between classical neural networks and quantum computing, many questions remain unanswered. If the expressivity of Boltzmann machine states is not restricted by entanglement in the same way that MPS and tensor-network states are, what is the best way of understanding their limitations? How can physicists use the correspondence between ConvAC and TN to their advantage in finding efficient, expressive representations of many-body wave functions? Can classical data distributions be learned more efficiently by quantum GAN than classical GAN? Whatever the outcome of these and many other related questions, this promises to be an exciting and active area of research in the years to come.
Quantum Machine Learning (QML) and Quantum Deep Learning (QDL) are emerging research areas that combine quantum computing with machine learning and deep learning techniques.These approaches aim to improve computational speed, feature representation, optimisation, and learning performance in complex data-driven problems.This review paper presents a structured discussion of recent developments in QML and QDL, focusing on major algorithms, application areas, implementation approaches, current limitations, and future research directions.The review covers important quantum-based learning methods, including quantum support vector machines, quantum k-nearest neighbours, quantum principal component analysis, quantum neural networks, variational quantum classifiers, quantum convolutional neural networks, quantum reinforcement learning, quantum generative models, and hybrid quantum-classical models.The paper also discusses how these methods are being explored in healthcare, finance, cybersecurity, communication networks, image processing, natural language processing, and optimisation.However, the review shows that most QML and QDL models are still in the early stages of research.Current challenges include noisy quantum hardware, limited qubit count, data encoding issues, circuit design problems, difficulties with model training, and a lack of standardised benchmarks.The review concludes that QML and QDL have strong future potential, but their practical success depends on improved hardware, stronger algorithms, reliable frameworks, and fair comparison with classical models.
Deep quantum learning (DQL) is an emerging interdisciplinary field that bridges the realms of quantum computing and deep learning. By integrating the principles of quantum mechanics into deep neural networks, DQL seeks to harness the unique capabilities of quantum systems to revolutionize the landscape of machine learning and artificial intelligence. Quantum neural networks (QNNs) lie at the heart of DQL, utilizing quantum gates and entanglement to process classical data in quantum states. Quantum embeddings and quantum data preprocessing techniques are employed to encode classical information into quantum probability distributions, enabling quantum algorithms to manipulate classical data efficiently. Furthermore, hybrid quantum-classical optimization methods facilitate the training of QNNs by combining classical optimization techniques with quantum circuits. DQL shows great promise in solving computationally complex problems and may drive advancements in various fields, such as chemistry, optimization, and pattern recognition.
In this study, we explore the innovative domain of Quantum Federated Learning (QFL) as a framework for training Quantum Machine Learning (QML) models via distributed networks. Conventional machine learning models frequently grapple with issues about data privacy and the exposure of sensitive information. Our proposed Federated Quantum Neural Network (FedQNN) framework emerges as a cutting-edge solution, integrating the singular characteristics of QML with the principles of classical federated learning. This work thoroughly investigates QFL, underscoring its capability to secure data handling in a distributed environment and facilitate cooperative learning without direct data sharing. Our research corroborates the concept through experiments across varied datasets, including genomics and healthcare, thereby validating the versatility and efficacy of our FedQNN framework. The results consistently exceed 86% accuracy across three distinct datasets, proving its suitability for conducting various QML tasks. Our research not only identifies the limitations of classical paradigms but also presents a novel framework to propel the field of QML into a new era of secure and collaborative innovation.