Training machine learning models on classical computers is usually a time and compute intensive process. With Moore's law nearing its inevitable end and an ever-increasing demand for large-scale data analysis using machine learning, we must leverage non-conventional computing paradigms like quantum computing to train machine learning models efficiently. Adiabatic quantum computers can approximately solve NP-hard problems, such as the quadratic unconstrained binary optimization (QUBO), faster than classical computers. Since many machine learning problems are also NP-hard, we believe adiabatic quantum computers might be instrumental in training machine learning models efficiently in the post Moore's law era. In order to solve problems on adiabatic quantum computers, they must be formulated as QUBO problems, which is very challenging. In this paper, we formulate the training problems of three machine learning models-linear regression, support vector machine (SVM) and balanced k-means clustering-as QUBO problems, making them conducive to be trained on adiabatic quantum computers. We also analyze the computational complexities of our formulations and compare them to corresponding state-of-the-art classical approaches. We show that the time and space complexities of our formulations are better (in case of SVM and balanced k-means clustering) or equivalent (in case of linear regression) to their classical counterparts.
Training machine learning models on classical computers is usually a time and compute intensive process. With Moore's law nearing its inevitable end and an ever-increasing demand for large-scale data analysis using machine learning, we must leverage non-conventional computing paradigms like quantum computing to train machine learning models efficiently. Adiabatic quantum computers can approximately solve NP-hard problems, such as the quadratic unconstrained binary optimization (QUBO), faster than classical computers. Since many machine learning problems are also NP-hard, we believe adiabatic quantum computers might be instrumental in training machine learning models efficiently in the post Moore's law era. In order to solve problems on adiabatic quantum computers, they must be formulated as QUBO problems, which is very challenging. In this paper, we formulate the training problems of three machine learning models-linear regression, support vector machine (SVM) and balanced k-means clustering-as QUBO problems, making them conducive to be trained on adiabatic quantum computers. We also analyze the computational complexities of our formulations and compare them to corresponding state-of-the-art classical approaches. We show that the time and space complexities of our formulations are better (in case of SVM and balanced k-means clustering) or equivalent (in case of linear regression) to their classical counterparts.
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.
A constantly increasing number of parameters in modern machine learning models has become a significant bottleneck in their efficient training, resulting in a disproportionate consumption of resources, expressed in terms of energy and computational time. The vast majority of such resources are allocated to the training phase rather than the inference stage, leading to an inefficient process [1] , [2] , [3] . This study addresses this problem by introducing a quantum alternative for training machine learning models, formalized as a Quadratic Unconstrained Binary Optimization ( QUBO ) problem. Adiabatic quantum computers have shown promise in approximately solving certain NP -hard problems, such as QUBO , potentially offering speed advantages over classical computers in specific scenarios [ 4 , 5, [6] , [7] ]. Given that many machine learning problems are also NP -hard, adiabatic quantum computers could play a pivotal role in efficiently training machine learning models. Furthermore, inspired by the ones’ complement binary numeral system, this work includes the proposal of an efficient binary-to-decimal encoding, which improves data representation in the quantum context. A concrete implementation of a regression training problem on specific quantum hardware is also presented here, the results of which suggest that the adoption of quantum techniques in model training allows not only to address the problem of parameter explosion but also to offer promising prospects for significantly accelerate the training process by exploiting the unique properties of quantum computation.
Abstract Support vector machine (SVM) is a powerful supervised machine learning model that is often used in binary classification algorithms. As Moore’s Law approaches its theoretical limits and the demand for machine learning to handle large-scale, high-dimensional data analysis intensifies, the necessity of adopting non-traditional computational approaches becomes evident. Quantum computing, in particular, emerges as a vital solution for the effective training of SVM models, providing capabilities beyond those of classical computing systems. To solve the above problems, a QUBO (quadratic unconstrained binary optimization) model is proposed to transform the SVM machine learning model into a quadratic unconstrained binary optimization problem so that they can be effectively trained on the D-Wave platform using adiabatic quantum computer. The results show that the QUBO model can transform the SVM model into a simple quadratic programming problem, which makes it suitable for adiabatic quantum computer processing. When processing large-scale and high-dimensional data, this transformation shows a natural advantage and significantly improves computational efficiency. The application potential of this transformation technology is huge in the medical field.
A major challenge in machine learning is the computational expense of training these models. Model training can be viewed as a form of optimization used to fit a machine learning model to a set of data, which can take up significant amount of time on classical computers. Adiabatic quantum computers have been shown to excel at solving optimization problems, and therefore, we believe, present a promising alternative to improve machine learning training times. In this paper, we present an adiabatic quantum computing approach for training a linear regression model. In order to do this, we formulate the regression problem as a quadratic unconstrained binary optimization (QUBO) problem. We analyze our quantum approach theoretically, test it on the D-Wave adiabatic quantum computer and compare its performance to a classical approach that uses the Scikit-learn library in Python. Our analysis shows that the quantum approach attains up to [Formula: see text] speedup over the classical approach on larger datasets, and performs at par with the classical approach on the regression error metric. The quantum approach used the D-Wave 2000Q adiabatic quantum computer, whereas the classical approach used a desktop workstation with an 8-core Intel i9 processor. As such, the results obtained in this work must be interpreted within the context of the specific hardware and software implementations of these machines.
Quantum computing holds significant potential to accelerate machine learning algorithms, especially in solving optimization problems like those encountered in Support Vector Machine (SVM) training. However, current QUBO-based Quantum SVM (QSVM) methods rely solely on binary optimal solutions, limiting their ability to identify fuzzy boundaries in data. Additionally, the limited qubit count in contemporary quantum devices constrains training on larger datasets. In this paper, we propose a probabilistic quantum SVM training framework suitable for Coherent Ising Machines (CIMs). By formulating the SVM training problem as a QUBO model, we leverage CIMs' energy minimization capabilities and introduce a Boltzmann distribution-based probabilistic approach to better approximate optimal SVM solutions, enhancing robustness. To address qubit limitations, we employ batch processing and multi-batch ensemble strategies, enabling small-scale quantum devices to train SVMs on larger datasets and support multi-class classification tasks via a one-vs-one approach. Our method is validated through simulations and real-machine experiments on binary and multi-class datasets. On the banknote binary classification dataset, our CIM-based QSVM, utilizing an energy-based probabilistic approach, achieved up to 20% higher accuracy compared to the original QSVM, while training up to 104 times faster than simulated annealing methods. Compared with classical SVM, our approach either matched or reduced training time. On the IRIS three-class dataset, our improved QSVM outperformed existing QSVM models in all key metrics. As quantum technology advances, increased qubit counts are expected to further enhance QSVM performance relative to classical SVM.
Machine learning is a branch of Artificial Intelligence that seeks to make machines learn from data. It is being applied for solving real world problems with huge amount of data. Though, Machine Learning is receiving wide acceptance, however, execution time is one of the major concerns in practical implementations of Machine Learning techniques. It largely comprises of a set of techniques that trains a model by reducing the error between the desired or actual outcome and an estimated or predicted outcome, which is often called as loss function. Thus, training in machine learning techniques often requires solving a difficult optimization problem, which is the most expensive step in the entire model-building process and its applications. One of the possible solutions in near future for reducing execution time of training process in Machine learning techniques is to implement them on quantum computers instead of classical computers. It is conjectured that quantum computers may be exponentially faster than classical computers for solving problems which involve matrix operations. Some of the machine learning techniques like support vector machines make extensive use of matrices, which can be made faster by implementing them on quantum computers. However, their efficient implementation is non-trivial and requires existence of quantum memories. Thus, another possible solution in near term is to use a hybrid of Classical Quantum approach, where a machine learning model is implemented in classical computer but the optimization of loss function during training is performed on quantum computer instead of classical computer. Several Quantum optimization algorithms have been proposed in recent years, which can be classified as gradient based and gradient free optimization techniques. Gradient based techniques require the nature of optimization problem being solved to be convex, continuous and differentiable otherwise if the problem is non-convex then they can find local optima only whereas gradient free optimization techniques work well even with non-continuous, non-linear and nonconvex optimization problems. This chapter discusses a global optimization technique based on Adiabatic Quantum Computation (AQC) to solve minimization of loss function without any restriction on its structure and the underlying model, which is being learned. Further, it is also shown that in the proposed framework, AQC based approach would be superior to circuit-based approach in solving global optimization problems.