Entangled states proved to be an essential resource for information processing, however, its classification is still an open problem. The objective of this work is to apply machine learning methods based on distance metrics to make a quantum state classification. The classification method implementation was made using classical and quantum algorithms also comparing the performance and efficiency of both. However, it should be noted that all quantum computation processes made in this work used simulators provided by the SDK Qiskit. No real quantum computers were used to implement the quantum methods due to the qubit quantity that exceeds the available open-access quantum computers of the IBM Q-Experience. The classical results obtained in this work make a good classification of quantum states with a precision rate between 70% and 80%. The quantum predictions may have a lower precision, due to some simplifications made in the data pre-processing step, showing that quantum algorithms for entanglement classification probably will require a higher number of qubits than the currently available ones.
Entangled states proved to be an essential resource for information processing, however, its classification is still an open problem. The objective of this work is to apply machine learning methods based on distance metrics to make a quantum state classification. The classification method implementation was made using classical and quantum algorithms also comparing the performance and efficiency of both. However, it should be noted that all quantum computation processes made in this work used simulators provided by the SDK Qiskit. No real quantum computers were used to implement the quantum methods due to the qubit quantity that exceeds the available open-access quantum computers of the IBM Q-Experience. The classical results obtained in this work make a good classification of quantum states with a precision rate between 70% and 80%. The quantum predictions may have a lower precision, due to some simplifications made in the data pre-processing step, showing that quantum algorithms for entanglement classification probably will require a higher number of qubits than the currently available ones.
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.
A powerful way to improve performance in machine learning is to construct an ensemble that combines the predictions of multiple models. Ensemble methods are often much more accurate and lower variance than the individual classifiers that make them up but have high requirements in terms of memory and computational time. In fact, a large number of alternative algorithms is usually adopted, each requiring to query all available data. We propose a new quantum algorithm that exploits quantum superposition, entanglement and interference to build an ensemble of classification models. Thanks to the generation of the several quantum trajectories in superposition, we obtain B transformations of the quantum state which encodes the training set in only log(B) operations. This implies exponential growth of the ensemble size while increasing linearly the depth of the correspondent circuit. Furthermore, when considering the overall cost of the algorithm, we show that the training of a single weak classifier impacts additively the overall time complexity rather than multiplicatively, as it usually happens in classical ensemble methods. We also present small-scale experiments on real-world datasets, defining a quantum version of the cosine classifier and using the IBM qiskit environment to show how the algorithms work.
Abstract A powerful way to improve performance in machine learning is to construct an ensemble that combines the predictions of multiple models. Ensemble methods are often much more accurate and have a lower variance than the individual classifiers that make them up, but have high requirements in terms of memory and computational time. In fact, a large number of alternative algorithms is usually adopted, each requiring to query all available data. We propose a new quantum algorithm that exploits quantum superposition, entanglement and interference to build an ensemble of classification models. Thanks to the generation of the several quantum trajectories in superposition, we obtain B transformations of the quantum state which encodes the training set in only log ( B ) operations. This implies an exponential growth of the ensemble size while increasing linearly the depth of the correspondent circuit. Furthermore, when considering the overall cost of the algorithm, we show that the training of a single weak classifier impacts additively to the overall time complexity rather than multiplicatively, as it usually happens in classical ensemble methods. We also present small-scale experiments on real-world datasets, defining a quantum version of the cosine classifier and using the IBM qiskit environment to show how the algorithms work.
It is a fundamental, but still elusive question whether methods based on quantum mechanics, in particular on quantum entanglement, can be used for classical information processing and machine learning. Even partial answer to this question would bring important insights to both fields of both machine learning and quantum mechanics. In this work, we implement simple numerical experiments, related to pattern/images classification, in which we represent the classifiers by quantum matrix product states (MPS). Classical machine learning algorithm is then applied to these quantum states. We explicitly show how quantum features (i.e., single-site and bipartite entanglement) can emerge in such represented images; entanglement characterizes here the importance of data, and this information can be practically used to improve the learning procedures. Thanks to the low demands on the dimensions and number of the unitary matrices, necessary to construct the MPS, we expect such numerical experiments could open new paths in classical machine learning, and shed at same time lights on generic quantum simulations/computations.
Machine learning can be used as a systematic method to non-algorithmically program quantum computers. Quantum machine learning enables us to perform computations without breaking down an algorithm into its gate building blocks, eliminating that difficult step and potentially reducing unnecessary complexity. In addition, the machine learning approach is robust to both noise and to decoherence, which is ideal for running on inherently noisy NISQ devices which are limited in the number of qubits available for error correction. Here we apply our prior work in quantum machine learning technique, to create a QGAN, a quantum analog to the classical Stylenet GANs developed by Kerras for image generation and classification. A quantum system is used as a generator and a separate quantum system is used as a discriminator. The generator Hamiltonian quantum parameters are augmented by quantum style parameters which play the role of the style parameters used by Kerras. Both generator parameters are trained in a GAN MinMax problem along with quantum parameters of the discriminator Hamiltonian. We choose a problem to demonstrate the QGAN that has purely quantum information. The task is to generate and discriminate quantum product states. Real product states are generated to be detected and separated from fake quantum product states generated by the quantum generator. The problem of detecting quantum product states is chosen to demonstrate the QGAN because is well known as purely quantum mechanical, has no classical analog and is an open problem for quantum product states of more than 2 qubits. With proper encoding of image pixels into quantum states as density matrices, the method demonstrated here is applicable to GAN image generation and detection that can be hosted on and take advantage of the nature of quantum computers.
Machine Learning (ML) aims at designing models that learn from previous experience, without being explicitly formulated. Applications of machine learning are inexhaustible, including recognizing patterns, predicting future trends and making decisions, and they are capable of handling sizable quantities of multi-dimensional data in the form of large vectors and tensors. To perform these operations on classical computers, however, requires vast time and computational resources. Unlike the classical computers that rely on computations using binary bits, Quantum Computers (QC) benefit from qubits which can hold combinations of 0 and 1 at the same time via superposition and entanglement. This makes QCs powerful at handling and post processing large tensors, making them a prime target for implementing ML algorithms. While several models used for ML on QCs are based on concepts from their classical computing counterparts, utilization of the QC's potential has made them the superior of the two. This paper presents an overview of the current state of knowledge in application of ML on QC, and evaluates the speed up, and complexity advantages of using quantum machines.