Improvising the performance of machine learning for applications in the field of computer science leads to create new algorithms. As these are being optimized, using the algorithms of the classical machine learning in the area of quantum computing are being widely researched. First, we can consider general optimization problems with only functional Evaluations. Quantum Speedups of the problems can be improved compared to the classical algorithms. A frame work for quantum inspired classical algorithms can be introduced. To study the various problems on quantum computers on testing properties and compare the quantum speed ups with the classical counter parts.
Improvising the performance of machine learning for applications in the field of computer science leads to create new algorithms. As these are being optimized, using the algorithms of the classical machine learning in the area of quantum computing are being widely researched. First, we can consider general optimization problems with only functional Evaluations. Quantum Speedups of the problems can be improved compared to the classical algorithms. A frame work for quantum inspired classical algorithms can be introduced. To study the various problems on quantum computers on testing properties and compare the quantum speed ups with the classical counter parts.
The theories of optimization and machine learning answer foundational questions in computer science and lead to new algorithms for practical applications. While these topics have been extensively studied in the context of classical computing, their quantum counterparts are far from well-understood. In this thesis, we explore algorithms that bridge the gap between the fields of quantum computing and machine learning. First, we consider general optimization problems with only function evaluations. For two core problems, namely general convex optimization and volume estimation of convex bodies, we give quantum algorithms as well as quantum lower bounds that constitute the quantum speedups of both problems to be polynomial compared to their classical counterparts. We then consider machine learning and optimization problems with input data stored explicitly as matrices. We first look at semidefinite programs and provide quantum algorithms with polynomial speedup compared to the classical state-of-the-art. We then move to machine learning and give the optimal quantum algorithms for linear and kernel-based classifications. To complement with our quantum algorithms, we also introduce a framework for quantum-inspired classical algorithms, showing that for low-rank matrix arithmetics there can only be polynomial quantum speedup. Finally, we study statistical problems on quantum computers, with the focus on testing properties of probability distributions. We show that for testing various properties including L1-distance, L2-distance, Shannon and Renyi entropies, etc., there are polynomial quantum speedups compared to their classical counterparts. We also extend these results to testing properties of quantum states.
The convergence of machine learning (ML) and quantum computing is quickly becoming a game-changing new frontier in computational science. The most intriguing area of overlap may be quantum optimization, which seeks to reduce the exponentially increasing complexity and computational cost of ML algorithms. As they grow larger and more complicated, traditional optimization methods, particularly in high-dimensional and non-convex space, will inevitably hit performance limits. Quantum optimization is the whole new paradigm that leverages quantum mechanical effects like superposition, entanglement, and tunnelling to explore solution spaces more efficiently. The chapter outlines the theory, practice, and potential of hybrid quantum-classical optimization algorithms for machine learning. The most brilliant research direction in the current NISQ (noisy intermediate-scale quantum) era is mixed systems leveraging classical computing capability augmented by quantum capacity. In such designs, computationally intensive subroutines like optimization for global optima or escape from local minima are left to quantum processors and data preprocessing, iterative refinement, and model testing are performed by classical processors. We start by defining the fundamental principles of quantum computing and acquainting readers with the fundamentals like qubits, quantum gates, and quantum circuits. These are the building blocks for quantum algorithms, which hopefully can be utilized for optimization, for example, the QAOA (quantum approximate optimization algorithm), the VQE (variational quantum Eigensolver), and quantum annealing. They all build to optimize the problems in some way differently: QAOA through parameterized quantum circuits, VQE through approximations of ground states of the Hamiltonians, and quantum annealing through quantum evolution to low-energy solutions. We then form a loop between these quantum algorithms and regular machine learning tasks. Optimization impacts virtually all ML phases, from training neural networks, where one reduces loss functions; feature selection, where one aims to discover the most relevant subset of input variables; and hyperparameter optimization, which often involves expensive search procedures over extremely large combinatorial spaces. Quantum optimization techniques can therefore, in principle, accelerate such procedures through computational complexity reduction and enhancing solutions over challenging landscapes. Realistic simulations and case studies emphasize the degree to which hybrid quantum-classical algorithms have been employed in solving ML problems, that is, QSVMs, quantum-enhanced clustering, and quantum reinforcement learning. Despite their experimental nature, these applications already show encouraging results in terms of improved performance metrics as well as reduction in time-to-solution compared to classical-only solutions. Notwithstanding that, this new field is not bereft of real challenges. Quantum hardware suffers from hard limits on qubit fidelity, decoherence, and scalability in the current times. Furthermore, quantum circuit integration into broad ML pipelines requires novel architectures and software platforms. As a counter to those issues, this chapter surveys recent advances in quantum programming languages, simulators, and hybrid platforms like PennyLane, Qiskit, and TensorFlow Quantum. We conclude by looking to the future possibility that quantum optimization will revolutionize the machine learning landscape. As hardware improves and algorithmic complexity increases, the possibility of quantum-powered learning systems solving hard problems becomes increasingly accessible. From speeding up deep network training to enabling new types of unsupervised learning, quantum optimization holds the potential to recast computational tractability in machine learning. This chapter is an all-encompassing introduction and state-of-the-art work for students, researchers, and practitioners interested in using quantum optimization for practical ML applications. It sets the foundation for understanding how to pursue hybrid approaches (how they may be applied today in the real world and bracing oneself for disruption in the future).
In this chapter, the authors discuss the use of quantum computing concepts to optimize the decision-making capability of classical machine learning algorithms. Machine learning, a subfield of artificial intelligence, implements various techniques to train a computer to learn and adapt to various real-time tasks. With the volume of data exponentially increasing, solving the same problems using classical algorithms becomes more tedious and time consuming. Quantum computing has varied applications in many areas of computer science. One such area which has been transformed a lot through the introduction of quantum computing is machine learning. Quantum computing, with its ability to perform tasks in logarithmic time, aids in overcoming the limitations of classical machine learning algorithms.
In this chapter, the authors discuss the use of quantum computing concepts to optimize the decision-making capability of classical machine learning algorithms. Machine learning, a subfield of artificial intelligence, implements various techniques to train a computer to learn and adapt to various real-time tasks. With the volume of data exponentially increasing, solving the same problems using classical algorithms becomes more tedious and time consuming. Quantum computing has varied applications in many areas of computer science. One such area which has been transformed a lot through the introduction of quantum computing is machine learning. Quantum computing, with its ability to perform tasks in logarithmic time, aids in overcoming the limitations of classical machine learning algorithms.
Encouraged by growing computing power and algorithmic development, machine learning technologies have become powerful tools for a wide variety of application areas, spanning from agriculture to chemistry and natural language processing. The use of quantum systems to process classical data using machine learning algorithms has given rise to an emerging research area, i.e. quantum machine learning. Despite its origins in the processing of classical data, quantum machine learning also explores the use of quantum phenomena for learning systems, the use of quantum computers for learning on quantum data and how machine learning algorithms and software can be formulated and implemented on quantum computers. Quantum machine learning can have a transformational effect on computer science. It may speed up the processing of information well beyond the existing classical speeds. Recent work has seen the development of quantum algorithms that could serve as foundations for machine learning applications. Despite its great promise, there are still significant hardware and software challenges that need to be resolved before quantum machine learning becomes practical. In this paper, we present an overview of quantum machine learning in the light of classical approaches. Departing from foundational concepts of machine learning and quantum computing, we discuss various technical contributions, strengths and similarities of the research work in this domain. We also elaborate upon the recent progress of different quantum machine learning approaches, their complexity, and applications in various fields such as physics, chemistry and natural language processing.
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.