Recently, the several applications of the probabilistic model based on two of the main concepts in quantum physics - a density matrix and the Born rule, have been introduced. It was shown that the model can be suitable for the modeling of learning algorithms in biologically plausible artificial neural networks framework, like it is the case of on-line learning algorithms for Independent /Principal/Minor Component Analysis, which could be realized on parallel hardware based on very simple computational units. Also, it has been shown that the quantum entropy of the system, related to that model, can be successfully used in the problems like change point detection, with some examples of applications in the area of power electronics and general classification problems. Here, we present a robust on-line Principal Component Algorithm based on the proposed model, which extracts several principal components simultaneously. Also, we will show usefulness of the proposed method in a simple example of image segmentation.
Recently, the several applications of the probabilistic model based on two of the main concepts in quantum physics - a density matrix and the Born rule, have been introduced. It was shown that the model can be suitable for the modeling of learning algorithms in biologically plausible artificial neural networks framework, like it is the case of on-line learning algorithms for Independent /Principal/Minor Component Analysis, which could be realized on parallel hardware based on very simple computational units. Also, it has been shown that the quantum entropy of the system, related to that model, can be successfully used in the problems like change point detection, with some examples of applications in the area of power electronics and general classification problems. Here, we present a robust on-line Principal Component Algorithm based on the proposed model, which extracts several principal components simultaneously. Also, we will show usefulness of the proposed method in a simple example of image segmentation.
Recently, it has been shown that a probabilistic model based on two of the main concepts in quantum physics - a density matrix and the Born rule, can be suitable for the modeling of learning algorithms in biologically plausible artificial neural networks framework. It has been shown that the proposed probabilistic interpretation is suitable for modeling on-line learning algorithms for Independent /Principal/Minor Component Analysis, which could be realized on parallel hardware based on very simple computational units. Also, it has been shown that the quantum entropy of the system, related to that model, can be successfully used in the problems like change point detection. Here, it will be shown that the proposed model can be successfully used in other areas of applied signal processing, with some examples of applications in the area of power electronics and general classification problems.
In this paper, we introduce elements of probabilistic model that is suitable for modeling of learning algorithms in biologically plausible artificial neural networks framework. Model is based on two of the main concepts in quantum physics - a density matrix and the Born rule. As an example, we will show that proposed probabilistic interpretation is suitable for modeling of on-line learning algorithms for PSA, which are preferably realized by a parallel hardware based on very simple computational units. Proposed concept (model) can be used in the context of improving algorithm convergence speed, learning factor choice, or input signal scale robustness. We are going to see how the Born rule and the Hebbian learning rule are connected
It is well known that the field of pattern recognition is concerned with the automatic discovery of regularities in data through the use of computer algorithms and with the use of these regularities to take actions such as classifying the data into different categories. There are many algorithms based on different theoretical backgrounds that could be used for pattern recognition in practical applications. Generally, most of the algorithms are applied in areas like classification, regression or change point detection.Recently, it has been shown that a probabilistic model based on two of the main concepts in quantum physics – a density matrix and the Born rule, can be suitable for the modeling of learning algorithms in biologically plausible artificial neural networks framework. It has been shown that the proposed probabilistic interpretation is suitable for modeling on-line learning algorithms for Independent/Principal/Minor Component Analysis, which could be realized on parallel hardware based on very simple computational units. Also, it has been shown that the quantum entropy of the system, related to that model, can be successfully used in the problems like change point or anomalies detection as well as simple classification problems. Here another application of the proposed quantum probabilistic model is going to be presented. A general paradigm called QLEAR learning (Quantum Low Entropy based Associative Reasoning) would be presented and tested in classification context. Proposed method potentially can overcome the problem that classifier performance depends greatly on the characteristics of the data to be classified. It is known that until now, there is no single classifier that works best on all given problems (a phenomenon that may be explained by the no-free-lunch theorem). Here we will try to propose a classification algorithm that, actually, automatically adjusts its performance according to characteristics of the data on which it is applied. An interesting aspect is that proposed method inherently solves the problem of unbalanced classes (classes that have significantly different size). The proposed paradigm can be applied in any area in which standard classification techniques are applied. The method is going to be analyzed in the context of classification, prediction and solving some mathematical problems.We’ll analyze, mainly, the case in which data is represented by vectors. Generalization toward multiway data would be discussed only on one example. The approach is based on the idea that classification can be understood as supervised clustering, where quantum entropy, in the context of the quantum probabilistic model, will be used as a “capturer” (measure, or external index) of the “natural structure” of the data. By using quantum entropy we don’t make any assumption about linear separability of the data that are going to be classified. The basic idea is to find close neighbours to a query sample and then use relative change in the quantum entropy as a measure of similarity of the newly arrived sample with the representatives of interest. In other words, method is based on calculation of quantum entropy of the referent system and its relative change with the addition of the newly arrived sample. Referent system consists of vectors/matrices that represent individual classes and that are the most similar, in Euclidean distance sense, to the vector that is analyzed. The classification problem is analysed in the context of measuring similarities to prototype examples of categories. The proposed method could be seen as a hybrid of nearest neighbor and optimization machine learning technique which deals naturally with the multiclass setting, has reasonable computational complexity both in training and at run time, and yields excellent results in practice.
Quantum principal component analysis (QPCA) is analogous to the classical method with additive speedup. This is based on the unsupervised dimensionality reduction mechanism that transforms exponentially high dimensional data points into low dimensional space by retaining significant features with the largest variance. To our knowledge, quantum computations are highly exponential and supports implicit parallelism. Therefore, quantum method for finding principal components are proved to achieve exponential speedup over existing classical solution. An advantage of quantum superposition is utilized for the Eigen decomposition of density matrix which is identical to covariance, however, a way through which its computation happen, is truly an interesting factor. This paper presents basic methodological framework to design QPCA algorithm. Our framework includes the methods for quantum data encoding, quantum memory processing, and the requisite quantum circuit implementations to realize QPCA algorithms. In addition, we categorized existing QPCA methods in view of recent advances. We then proposed the possible advancements that can benefit to design quantum based efficient algorithms for principal component analysis. At the last, suggested concepts are compared with existing methods based on complexities and other factors to justify our proposal as significant in perspective to future directions.
This paper will review the basic building blocks of quantum computing and discuss the main applications in artificial intelligence that can be addressed more efficiently using the quantum computers of today. Artificial intelligence and quantum computing have many features in common. Quantum computing can provide artificial intelligence and machine learning algorithms with speed of training and computational power in less price. Artificial intelligence on the other hand can provide quantum computers with the necessary error correction algorithms. Some of the algorithms in AI that have been successfully implemented on a quantum computer, that we will present in this paper, are both unsupervised learning algorithms (clustering and Principal component analysis) and also supervised learning classification, such as support vector machines.
The teaching of physics is currently linked to the developments that occur in the field of computing; therefore, it cannot be ignored that new technologies are being developed from neural networks and evolving in terms of artificial intelligence. Physics has adopted these systems in order to be able to perform data processing, system analysis, image processing and signal classification in a more optimal way, which are applied in areas such as optics, astronomy, quantum mechanics, among others. In parallel, a relationship has been created between neural networks and quantum computing, for which this document seeks to investigate and delve into these structures and identify the links with quantum formalism. The established roadmap is developed from the construction and analysis of neural network algorithms, which are based on two main components, the activation functions and the self-regulation of statistical weights that structure the bases of machine learning, which allows multidisciplinary research between computational physics and quantum mechanics for the optimization and evolution of the concept of "classical" neural network, affirming to date the inexistence of a quantum system of the neural network, but the conceptual and mathematical association bases for the future development of the concept of the quantum neural network, in this way, based on the use of fundamental concepts of quantum mechanics, it is possible to blur the abstract nature of said physical theory and reflect the applicability in machine learning, a potential field for the development of artificial intelligence.