In the field of machine learning, vector quantization is a category of low-complexity approaches that are nonetheless powerful for data representation and clustering or classification tasks. Vector quantization is based on the idea of representing a data or a class distribution using a small set of prototypes, and hence, it belongs to interpretable models in machine learning. Further, the low complexity of vector quantizers makes them interesting for the application of quantum concepts for their implementation. This is especially true for current and upcoming generations of quantum devices, which only allow the execution of simple and restricted algorithms. Motivated by different adaptation and optimization paradigms for vector quantizers, we provide an overview of respective existing quantum algorithms and routines to realize vector quantization concepts, maybe only partially, on quantum devices. Thus, the reader can infer the current state-of-the-art when considering quantum computing approaches for vector quantization.
In the field of machine learning, vector quantization is a category of low-complexity approaches that are nonetheless powerful for data representation and clustering or classification tasks. Vector quantization is based on the idea of representing a data or a class distribution using a small set of prototypes, and hence, it belongs to interpretable models in machine learning. Further, the low complexity of vector quantizers makes them interesting for the application of quantum concepts for their implementation. This is especially true for current and upcoming generations of quantum devices, which only allow the execution of simple and restricted algorithms. Motivated by different adaptation and optimization paradigms for vector quantizers, we provide an overview of respective existing quantum algorithms and routines to realize vector quantization concepts, maybe only partially, on quantum devices. Thus, the reader can infer the current state-of-the-art when considering quantum computing approaches for vector quantization.
Abstract Prototype-based models like the Generalized Learning Vector Quantization (GLVQ) belong to the class of interpretable classifiers. Moreover, quantum-inspired methods get more and more into focus in machine learning due to its potential efficient computing. Further, its interesting mathematical perspectives offer new ideas for alternative learning scenarios. This paper proposes a quantum computing-inspired variant of the prototype-based GLVQ for classification learning. We start considering kernelized GLVQ with real- and complex-valued kernels and their respective feature mapping. Thereafter, we explain how quantum space ideas could be integrated into a GLVQ using quantum bit vector space in the quantum state space Hn H n and show the relations to kernelized GLVQ. In particular, we explain the related feature mapping of data into the quantum state space Hn H n . A key feature for this approach is that Hn H n is an Hilbert space with particular inner product properties, which finally restrict the prototype adaptations to be unitary transformations. The resulting approach is denoted as Qu-GLVQ. We provide the mathematical framework and give exemplary numerical results.
Machine Learning (ML) aims at designing models that learn from previous experience, without being explicitly formulated. Applications of machine learning are inexhaustible, including recognizing patterns, predicting future trends and making decisions, and they are capable of handling sizable quantities of multi-dimensional data in the form of large vectors and tensors. To perform these operations on classical computers, however, requires vast time and computational resources. Unlike the classical computers that rely on computations using binary bits, Quantum Computers (QC) benefit from qubits which can hold combinations of 0 and 1 at the same time via superposition and entanglement. This makes QCs powerful at handling and post processing large tensors, making them a prime target for implementing ML algorithms. While several models used for ML on QCs are based on concepts from their classical computing counterparts, utilization of the QC's potential has made them the superior of the two. This paper presents an overview of the current state of knowledge in application of ML on QC, and evaluates the speed up, and complexity advantages of using quantum machines.
The goal of machine learning (ML) is to develop models that automatically learn from the past without being explicitly programmed. ML has numerous applications, such as pattern recognition, forecasting upcoming trends, and judgement. It can handle massive amounts of huge vectors and tensors representing multidimensional data. To handle these processes on traditional computers, enormous time and computational resources are required. Unlike traditional computers, which use binary bits to compute, quantum computers (Q.C.) use qubits, which can simultaneously hold 0 and 1 combinations through superposition and entanglement. This makes Q.Cs an excellent choice for implementing ML algorithms because they are skilled at handling and post-processing large tensors. Although many of the models used for ML on quantum computers are based on concepts from their classical computing counterparts, the use of quantum computers has made them the better of the two. This paper assess the speed and complexity benefits of using quantum computers and gives a general overview of the state of knowledge regarding the use of ML on Q.C.
Quantum computers acting as ML accelerators have attracted considerable interest as a promising avenue for addressing the limitations of classical computing confronted with solving complex, high-dimensional problems and handling large data sets. The most exciting aspect of quantum computing lies in its quantum advantage via techniques such as quantum parallelism, superposition, and entanglement which allows not only for rapid data processing, but also a means to resolve complex optimization problems beyond the capacity of classical algorithms. Nevertheless, the usage of quantum computing in machine learning is still a fledgling domain, with challenges concerning quantum noise, hardware restrictions, and algorithmic development. In particular, this research is concerned with the development of and study on hybrid quantum-classical algorithms that target to improve ML models in terms of computational capabilities by making use of the best of both worlds. To address this, researchers are developing hybrid algorithms that leverage the strengths of quantum computing for specific tasks, like optimization and pattern recognition, while still relying on classical computing for more flexible and larger-scale processing, ultimately achieving more efficient machine learning systems that can handle large datasets and complex problem-solving more effectively. It includes potential hybrid approaches like quantum-enhanced optimization algorithms, quantum neural networks, and quantum support vector machines, and examines how such algorithms can be used for practical ML problems including data classification, regression and clustering. Furthermore, the paper proposes that hybrid quantum algorithms offer several advantages over their classical counterparts, such as faster convergence rates, higher accuracy in high-dimensional spaces, and improved handling of non-linear and complex problem landscapes. Key advancements in the area of data processing speed and efficiency in problem-solving with and without quantum in the machine learning workflow are also highlighted in the research through comparative analysis and simulation studies. Lastly, the paper concludes by outlining the obstacles yet to be surmounted and the opportunities that lie ahead for hybrid quantum-classical algorithms, such as further improvement of quantum hardware and error mitigation methods, as well as the design of new algorithmic paradigms that seamlessly integrates the classical and quantum computing spaces.
Recently, increased availability of the data has led to advances in the field of machine learning. Despite of the growth in the domain of machine learning, the proximity to the physical limits of chip fabrication in classical computing is motivating researchers to explore the properties of quantum computing. Since quantum computers leverages the properties of quantum mechanics, it carries the ability to surpass classical computers in machine learning tasks. The study in this paper contributes in enabling researchers to understand how quantum computers can bring a paradigm shift in the field of machine learning. This paper addresses the concepts of quantum computing which influences machine learning in a quantum world. It also states the speedup observed in different machine learning algorithms when executed on quantum computers. The paper towards the end advocates the use of quantum application software and throw light on the existing challenges faced by quantum computers in the current scenario.
Quantum computing is an upcoming paradigm that has been in the transformation process in data science in the light of quantum physics. On that account, the present chapter delivers in-depth details on how quantum phenomena like superposition and entanglement could be brought to bear on data-intensive problems that are beyond classical computational means. Basic concepts such as qubits, gates, and circuits are studied with an emphasis on parallelism and interference to speed up computations. They look at the major applications for data science with a focus on 32 promising quantum machine-learning techniques: quantum support vector machines and quantum neural networks that promise a quantum speed-up in classifying and regressing data sets. It also looks at quantum methods for clustering, dimensionality reduction, and combinatorial optimization, including quantum annealing and the quantum approximate optimization algorithm, to name just a few, with respect to speed and accuracy. Therefore, quantum simulation is strongly promoted for the simulation of complicated systems, which are of interest, for example, in chemistry, materials science, and drug discovery. Besides, some shelves are kept for an overview of the interdisciplinary approaches of quantum computing with big data analytics and also with cryptography, including quantum-safe encryption. The hardware scalability stands as the main challenge, while the prime concern is error correction. Other than these issues, advances in investigating and developing are schema concepts for unleashing the power of quantum computing to change data science.