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Journal of Physics Conference Series

Comparisons of performance between quantum-enhanced and classical machine learning algorithms on the IBM Quantum Experience

Pavlo V. Zahorodko, Serhiy O. Semerikov, Vladimir Soloviev, Андрій Миколайович Стрюк, Mykola I. Striuk, Hаnnа M. Shalatska

Published Mar 1, 2021• 31 citations
Publisher

Abstract

Abstract Machine learning is now widely used almost everywhere, primarily for forecasting. In the broadest sense, the machine learning objective may be summarized as an approximation problem, and the issues solved by various training methods can be reduced to finding the optimal value of an unknown function or restoring a function. At the moment, we have only experimental samples of quantum computers based on classical-quantum logic, when quantum gates are used instead of ordinary logic gates, and probabilistic quantum bits are used instead of deterministic bits. Namely, the probabilistic nature problems that provide for the determination of a certain optimal state from a large set of possible ones on which quantum computers can achieve “quantum supremacy” – an extraordinary (by many orders of magnitude) reduction in the time required to solve the task. The main idea of the work is to identify the possibility of achieving, if not quantum supremacy, then at least a quantum advantage when solving machine learning problems on a quantum computer.

DOI
10.1088/1742-6596/1840/1/012021

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Abstract Machine learning is now widely used almost everywhere, primarily for forecasting. In the broadest sense, the machine learning objective may be summarized as an approximation problem, and the issues solved by various training methods can be reduced to finding the optimal value of an unknown function or restoring a function. At the moment, we have only experimental samples of quantum computers based on classical-quantum logic, when quantum gates are used instead of ordinary logic gates, and probabilistic quantum bits are used instead of deterministic bits. Namely, the probabilistic nature problems that provide for the determination of a certain optimal state from a large set of possible ones on which quantum computers can achieve “quantum supremacy” – an extraordinary (by many orders of magnitude) reduction in the time required to solve the task. The main idea of the work is to identify the possibility of achieving, if not quantum supremacy, then at least a quantum advantage when solving machine learning problems on a quantum computer.
All the data stored and processed by our computers is encoded as sequences of zeros and ones, called bits. Quantum computers offer an alternative to this traditional way of encoding and manipulating information. The information in a collection of qubits can be a combination, also called a superposition, over many possible sequences of zeros and ones. Where classical computation consists of flipping zeros and ones, quantum computation consists of manipulating high-dimensional vectors called quantum states. Researchers have found ways to use this to engineer quantum algorithms that solve some tasks much faster than any classical computer would. These are called quantum advantages, and are proven for specific tasks, such as breaking some encryption schemes and solving certain large linear systems. The goal of this thesis was to find new tasks for which quantum computers provably have an advantage over classical computers. In this thesis, I present two such advantages and associated results. The first one revolves around a physically relevant learning task. In other words, I explore how quantum computers can be used to help solve specialized machine learning tasks. The second one addresses the simulation of classical systems. One of the first high-potential and natural uses of quantum computers was the simulation of quantum systems. A lot of real-world problems, however, are ruled by classical physics. It turns out that quantum computers are well suited for the simulation of some exponentially large classical systems. In this thesis, I add a new problem to this list.
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).
The field of quantum computing aims to speed up the solution for certain computational problems using quantum computers. The key milestone in this field is the claim that quantum supremacy can be achieved using quantum computers which shows that the quantum speedup is achievable in a real time system. Quantum computing can improve the performance of machine learning algorithms based on the quantum algorithms by producing better solutions for machine learning tasks than classical machine learning approaches. This chapter provides an overview on quantum computing, quantum supremacy and recent research and inventions in the field. The paper additionally illustrates the research conducted with respect to impact of quantum computing on machine learning.
In this paper, we present a performance comparison of machine learning algorithms executed on traditional and quantum computers. Quantum computing has potential of achieving incredible results for certain types of problems, and we explore if it can be applied to machine learning. First, we identified quantum machine learning algorithms with reproducible code and had classical machine learning counterparts. Then, we found relevant data sets with which we tested the comparable quantum and classical machine learning algorithm's performance. We evaluated performance with algorithm execution time and accuracy. We found that quantum variational support vector machines in some cases had higher accuracy than classical support vector machines on multi-class classification problems. The main conclusion was that quantum multi-class SVM classifiers have the potential to be useful in the future as quantum computer’s available number of qubits increases.
Currently, pattern recognition is an extremely important activity in several fields.Approaches using artificial intelligence are one of the means of detecting these patterns and, therefore, optimizations in these methods are essential for such recognition to be carried out efficiently, both in processing time and in the hit rate.The field of machine learning, one of the paradigms of artificial intelligence, dates back to the beginnings of modern computing and in recent decades has been used intensively in pattern recognition.Despite the technical challenges related to the hardware, quantum computing has also been studied for a better performance of multiple computational tasks that are often unfeasible to be performed by classical algorithms.In this context, one of the fields that gain focus is the use of quantum circuits in machine learning algorithms.Thus, this work aims to compare the performance and complexity of classical algorithms, used in machine learning, to their quantum and hybrid versions, in order to identify the most efficient implementations.Another aspect to highlight is the feasibility of applying such models at certain scales, taking into account the limitations of current hardware.This will be done through a review of current academic production, followed by the development, implementation, testing, and analysis of the performance and complexity of both approaches.It is expected with this experiment that it will be possible to verify the effective possibility of using machine learning algorithms in their hybrid versions, either in current cases or in the near future.