Quantum machine learning is a research discipline intersecting quantum algorithms and machine learning. While a number of quantum algorithms with potential speedups have been proposed, it is quite difficult to provide evidence that quantum computers will be useful in solving real-world problems. Our work makes progress towards this goal. In this work we design quantum algorithms for dimensionality reduction and for classification and combine them to provide a quantum classifier that we test on the MNIST data set of handwritten digits. We simulate the quantum classifier, including errors in the quantum procedures, and show that it can provide classification accuracy of $98.5%$. The running time of the quantum classifier is only polylogarithmic in the dimension and number of data points. Furthermore, we provide evidence that the other parameters on which the running time depends scale favorably, ascertaining the efficiency of our algorithm.
Quantum machine learning is a research discipline intersecting quantum algorithms and machine learning. While a number of quantum algorithms with potential speedups have been proposed, it is quite difficult to provide evidence that quantum computers will be useful in solving real-world problems. Our work makes progress towards this goal. In this work we design quantum algorithms for dimensionality reduction and for classification and combine them to provide a quantum classifier that we test on the MNIST data set of handwritten digits. We simulate the quantum classifier, including errors in the quantum procedures, and show that it can provide classification accuracy of 98.5. The running time of the quantum classifier is only polylogarithmic in the dimension and number of data points. Furthermore, we provide evidence that the other parameters on which the running time depends scale favorably, ascertaining the efficiency of our algorithm.
Quantum machine learning has emerged as a promising frontier, leveraging the principles of quantum computing to enhance classical algorithms. This paper proposes an optimized Quantum Support Vector Classifier (QSVC) for the classification of the MNIST dataset (a benchmark in handwritten digit recognition). We employ a Chebyshev Parameterized Quantum Circuit (PQC) with an increased number of qubits and layers, and utilize an existing projected quantum kernel method to effectively capture the complex patterns in the data. To enhance model robustness, data augmentation techniques are applied, and dimensionality reduction is performed using Principal Component Analysis (PCA). The proposed QSVC demonstrates competitive accuracy on both the training and testing datasets, highlighting the potential of quantum kernel methods in practical machine learning applications. A comparative analysis with classical Support Vector Machines (SVM) demonstrates the feasibility of quantum methods for high-dimensional classification tasks. Additionally, we investigate the impact of varying the number of qubits in the quantum circuit, providing in-depth insights into the scalability and performance trade-offs of quantum kernel methods.
In this work, we investigate the use of a quantum circuit as a binary classification model in the context of quantum machine learning. We call this model, binary quantum classifier.
First, we describe fundamental concepts of quantum computing and introduce the computational tool used: Qibo, an open-source framework for efficient quantum simulations and quantum hardware control. Then, we describe how to design a binary quantum classifier for the classification of images and small arrays of variables by showing how to input data in the circuit, defining a quantum circuit model Ansatz with trainable parameters and a loss function, and implementing multiple minimizers. We test our quantum classifier with two data sets. The first one is the MNIST data set which is composed of handwritten digits (reduced to only handwritten zeros and handwritten ones for binary classification). We study the behavior of different minimizers by increasing the number of layers of the Ansatz. The second data set represents two different high energy collisions that can occur at colliders such as LHC (CERN). Due to in-time proton-proton interactions known as pile-up, we distinguish two different data sets: "without pile-up" and "with pile-up". These collisions can be represented by images of size 32x32 or by six high-level variables that we call features. By increasing the size of the training data set and the number of layers of the Ansatz, we search for the best minimizer. Splitting the data set in training set and test set, we compute: ROC curve, AUC score, confusion matrices and test set accuracy. For "with pile-up" images, we compare the results obtained with the quantum classifier with a small convolutional neural network.
We conclude that is possible to build a binary quantum classifier with a quantum circuit and we highlight its performances and limitations in comparison with classical technologies.
Quantum machine learning is a new field of study that aims to apply the advantages of quantum computing, such as superposition, which is one of the intriguing properties that could speed up computation, to machine learning. Like classical machine learning models, quantum machine learning models can learn from specific input data and perform specific prediction tasks. However, quantum machine learning models are currently in the form of quantum circuits with parameterizable gates. In this paper, the implementation of a quantum classification model is investigated using the two most well-known quantum machine learning development tools: Cirq with TensorFlow Quantum (TFQ) and Qiskit with PyTorch. The quantum classification circuit is trained to recognize images of handwritten digits using the MNIST dataset. However, because the quantum computer is still in development and is difficult to access and use, quantum simulators are the best alternative for the time being. The performance of the quantum classification model implemented by the two development tools is then compared in this paper experimentally using quantum simulators on two different hardware configurations. In addition, the experimental setups differ in the number of input qubits used to store the image’s classical pixel values. Finally, the wall time and CPU time used to run the training process, as well as classification accuracy, are examined. In terms of accuracy, Qiskit with PyTorch outperforms Cirq with TFQ only in the lower number of qubits but the results are similar in the higher number of qubits. The experiment results in terms of run-time are highly different. From the result, we find that Cirq is noticeably faster than Qiskit in every experiment by at least 90 times.
The evolution of quantum computers and quantum machine learning (QML) algorithms have started demonstrating exponential speed-ups. In machine learning problems, the efficient handling and manipulation of linear algebra subroutines defines the complexity of the task to be performed. Quantum computers handle big datasets in the form of vectors and matrix operations very efficiently. In this paper, quantum support vector machine (QSVM) algorithm is used to solve a classification problem using a benchmarking MNIST dataset of handwritten images of digits. Quantum SVM variational and kernel matrix algorithms are implemented to analyze quantum speedup on quantum simulator and physical quantum processor back-ends. The study compared classical and quantum SVM algorithms in terms of execution time and accuracy. The results explicitly prove quantum speed-up achieved by quantum classifiers on quantum back-ends for machine learning applications.
Nowadays, using machine learning for image classification is very common. However, due to the increasing demand for data processing and fast computing, the idea of enhancing machine learning with quantum computing has been proposed, known as quantum machine learning (QML). Quantum machine learning has the advantages of higher efficiency and accuracy. Quantum computing uses quantum bits (qubits) for data storage and computing, where a qubit can represent quantum states |0〉and |1〉simultaneously, enabling the processing of information for two states simultaneously, which is unparalleled in classical computing. Moreover, quantum machine learning can handle more complex data and process data faster. In classical machine learning, the processing of large-scale data and complex problems often faces problems of high computational complexity and low algorithm efficiency. Quantum computing can handle multiple computing tasks simultaneously, achieving faster computing. Therefore, in some scenarios that require efficient computing, quantum machine learning may be the best choice. In this study, we simulated quantum circuits using Qiskit and built a hybrid quantum-classical neural network model using VQNet to classify MNIST handwritten digits and CIFAR-10 datasets. The experiments showed that quantum machine learning has the advantages of efficiency, accuracy, and security over classical machine learning, which may be an improvement over classical machine learning. This research proposes a machine learning algorithm based on quantum computing, which promotes the development of quantum computing and quantum technology. At the same time, it provides a new solution and idea for image classification, enabling people to pursue faster and more accurate quantum machine learning instead of being limited to classical machine learning.[1]
In this work, we studied the use of Quantum Machine Learning (QML) algorithms for binary classification and compared their performance with classical Machine Learning (ML) methods. QML merges principles of Quantum Computing (QC) and ML, offering improved efficiency and potential quantum advantage in data-driven tasks and when solving complex problems. In binary classification, where the goal is to assign data to one of two categories, QML uses quantum algorithms to process large datasets efficiently. Quantum algorithms like Quantum Support Vector Machines (QSVM) and Quantum Neural Networks (QNN) exploit quantum parallelism and entanglement to enhance performance over classical methods. This study focuses on two common QML algorithms, Quantum Support Vector Classifier (QSVC) and QNN. We used the Qiskit software and conducted the experiments with three different datasets. Data preprocessing included dimensionality reduction using Principal Component Analysis (PCA) and standardization using scalers. The results showed that quantum algorithms demonstrated competitive performance against their classical counterparts in terms of accuracy, while QSVC performed better than QNN. These findings suggest that QML holds potential for improving computational efficiency in binary classification tasks. This opens the way for more efficient and scalable solutions in complex classification challenges and shows the complementary role of quantum computing.