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IEEE International Conference on Quantum Computing and Engineering (QCE)

Adiabatic Quantum Support Vector Machines

Dong Jun Woun, Prasanna Date

Published Sep 17, 2023• 3 citations
Publisher

Abstract

Machine learning's ability to analyze and predict complex data enables many scientific discoveries and industrial advances. However, state-of-the-art machine learning requires extensive computational resources for training. In machine learning, the training phase is crucial because it enables the model to acquire knowledge from the provided data. The duration of the training process varies significantly, ranging from a few hours to several months. As a result, the computational cost and time constraints hinder researchers from using machine learning. To address this issue, we investigated the possibility of using quantum computers for machine-learning tasks. We compared Date's [1] quantum support vector machine (SVM) approach on a D-Wave Advantage to a classical implementation on AMD Ryzen and Intel Xeon processors. We evaluated both the time-to-solution and the machine-learning performance of the quantum and classical systems. The results of our study demonstrated that SVMs scaled$O(N^{2})$on the quantum computer and$O(N^{2}d)$on the classical computer. Here, N represents the number of samples, and d represents the number of features. So, when trained with a data set with eight million features, we found that the quantum annealer outperformed the classical computer by 3.5-4.5x. The quantum approach maintained a comparable accuracy to the classical approach as well. In conclusion, quantum computers offer a computational advantage over classical computers for machine learning.

DOI
10.1109/qce57702.2023.10250

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Machine learning's ability to analyze and predict complex data enables many scientific discoveries and industrial advances. However, state-of-the-art machine learning requires extensive computational resources for training. In machine learning, the training phase is crucial because it enables the model to acquire knowledge from the provided data. The duration of the training process varies significantly, ranging from a few hours to several months. As a result, the computational cost and time constraints hinder researchers from using machine learning. To address this issue, we investigated the possibility of using quantum computers for machine-learning tasks. We compared Date's [1] quantum support vector machine (SVM) approach on a D-Wave Advantage to a classical implementation on AMD Ryzen and Intel Xeon processors. We evaluated both the time-to-solution and the machine-learning performance of the quantum and classical systems. The results of our study demonstrated that SVMs scaledO(N2)O(N^{2})O(N2)on the quantum computer andO(N2d)O(N^{2}d)O(N2d)on the classical computer. Here, N represents the number of samples, and d represents the number of features. So, when trained with a data set with eight million features, we found that the quantum annealer outperformed the classical computer by 3.5-4.5x. The quantum approach maintained a comparable accuracy to the classical approach as well. In conclusion, quantum computers offer a computational advantage over classical computers for machine learning.
Quantum machine learning is one of the fields where quantum computers are expected to bring advantages over classical methods. However, the limited size of current computers restricts the exploitation of the full potential of quantum machine learning methods. Additionally, different computing paradigms, both quantum and classical, each have their own strengths and weaknesses. Obtaining optimal results with algorithms thus requires algorithms to be tweaked to the underlying computational paradigm, and the tasks to be optimally distributed over the available computational resources. In this work, we explore the potential gains from combining different computing paradigms to solve the complex task of data classification for three different datasets. We use a gate-based quantum model to implement a quantum kernel and implement a complex feature map. Next, we formulate a quadratic unconstrained optimisation problem to be solved on quantum annealing hardware. We then evaluate the losses on classical hardware and reconfigure the model parameters accordingly. We tested this so-called triple-hybrid quantum support vector machine on various data sets, and find that it achieves higher precision than other support vector machines (both quantum and classical) on complex quantum data, whereas it achieves varying performance on simple classical data using limited training. For the complex data sets, the triple-hybrid version converges faster, requiring fewer circuit evaluations.
The current development of Support Vector Machines (SVM) has reached a bottleneck, with issues such as long training times and weak interpretability when dealing with large-scale, multi-dimensional data. This paper introduces the concept of Quantum Support Vector Machines (QSVM) and achieves efficient solutions through quantum algorithms such as the HHL algorithm. The research designs a computational architecture that combines classical and quantum computing, utilizing the Pauli decomposition of Hermitian matrices to simulate the quantum simulation of Hamiltonian quantities and implementing the quantum simulation of unitary operators. Based on the conclusions, a complete quantum linear solver circuit is designed, achieving exponential growth in computational complexity. Experiments using the Iris dataset demonstrate the excellent classification performance of QSVM, which outperform classical SVM in classification accuracy, computational time complexity, and memory requirements. More efficient quantum mapping algorithms and quantum circuit optimization methods are implemented, providing new ideas and methods for the application of SVM to large-scale datasets.
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.
The rapid growth of computer vision and increasingly complex image recognition tasks has exposed fundamental computational limitations of classical machine learning models, motivating the exploration of quantum computing as an emerging new paradigm. This paper presents a comprehensive benchmarking study of classical and quantum machine learning models for image recognition on the MNIST handwritten digit dataset, evaluating both traditional models, a Classical Support Vector Machine (CSVM) and a Quantum Support Vector Machine (QSVM), and deep neural network models, a Classical Convolutional Neural Network (CCNN) and a Quantum Convolutional Neural Network (QCNN), across four performance dimensions: classification accuracy, computational runtime, parameter count, and memory requirements. Experiments are conducted as functions of both feature dimensionality and sample size, and across CPU and GPU execution environments, providing a controlled, multidimensional comparison to address gaps in prior work. For the SVM-based models, QSVM consistently outperforms CSVM in accuracy, reaching ∼\sim∼ 0.90 versus ∼\sim∼ 0.85 at 1,000 samples, with a higher computational cost. A feature count of 10 qubits and a sample size in the range of 200 -- 500 emerge as practical operating points that balance accuracy and runtime. For the neural network models, CCNN and QCNN achieve comparable classification accuracy, both exceeding 0.96 at 64 features and 60,000 samples, yet QCNN offers superior parameter and memory efficiency at higher feature counts, while incurring higher runtime. Across both model families, quantum models consistently outperform classical models by greater margins in accuracy as feature dimensionality or sample size increases.
Quantum computing has been proven to excel in factorization issues and unordered search problems due to its capability of quantum parallelism. This unique feature allows exponential speed-up in solving certain problems. However, this advantage does not apply universally, and challenges arise when combining classical and quantum computing to achieve acceleration in computation speed. This paper aims to address these challenges by exploring the current state of quantum machine learning and benchmarking the performance of quantum and classical algorithms in terms of accuracy. Specifically, we conducted experiments with three datasets for binary classification, implementing Support Vector Machine (SVM) and Quantum SVM (QSVM) algorithms. Our findings suggest that the QSVM algorithm outperforms classical SVM on complex datasets, and the performance gap between quantum and classical models increases with dataset complexity, as simple models tend to overfit with complex datasets. While there is still a long way to go in terms of developing quantum hardware with sufficient resources, quantum machine learning holds great potential in areas such as unsupervised learning and generative models. Moving forward, more efforts are needed to explore new quantum learning models that can leverage the power of quantum mechanics to overcome the limitations of classical machine learning.
Machine learning model training, which ultimately optimizes a model’s cost function is usually a time- consuming and computationally intensive process on classical computers. This has been more intense due to the in- creased demand for large-scale data analysis, requiring unconventional computing paradigms like quantum computing to enhance training efficiency. Adiabatic quantum computers have excelled at solving optimization problems, which require the quadratic unconstrained binary optimization (QUBO) format of the problem of interest. In this study, the squared error minimization in the multiple linear regression model is reformulated as a QUBO problem enabling it to be solved using D-wave adiabatic quantum computers. Same formulation was used to obtain a solution using gate-based algorithms such as quantum approximate optimization algorithm (QAOA) and sampling variational quantum eigensolver (VQE) im- plemented via IBM Qiskit. The results obtained through these approaches in the context of runtime and mean squared error(MSE) were analyzed and compared to the classical approaches. Our experimental results indicate a runtime ad- vantage in the D-wave annealing approach over the classical Scikit learn regression approach. The time advantage can be observed when N>524288 compared to Sklearn Linear Regression and when N>65536 compared to Sklearn SGDRegressor. Support vector machine induced neural networks, where the margin-based entropy loss is converted into a QUBO with Lagrangian approach is also focused in this study concerning the applicability for nonlinear models.