In this paper we address the problem of using one probability space for estimating parameters and predicting future data when the observed data come from multiple contexts and thus from distinct spaces. We explain that a set-based probabilistic space might be suboptimal in the case of multiple contexts. To overcome suboptimality and reconcile multiple contexts in one space, the paper introduces the Quantum Probability Space (QPS). We also present an algorithm to calculate the QPS for data observed from multiple contexts and provide a web application that implements the algorithm. The QPS has application in Information Retrieval (IR), Machine Learning (ML) and in any domain where items should optimally be ranked and classified by some properties but under conditions of uncertainty due to context.
In this paper we address the problem of using one probability space for estimating parameters and predicting future data when the observed data come from multiple contexts and thus from distinct spaces. We explain that a set-based probabilistic space might be suboptimal in the case of multiple contexts. To overcome suboptimality and reconcile multiple contexts in one space, the paper introduces the Quantum Probability Space (QPS). We also present an algorithm to calculate the QPS for data observed from multiple contexts and provide a web application that implements the algorithm. The QPS has application in Information Retrieval (IR), Machine Learning (ML) and in any domain where items should optimally be ranked and classified by some properties but under conditions of uncertainty due to context.
Learning algorithms based on probability organize the observed data in subsets corresponding to binary variables. In this paper, we address the problem of estimating one probability space given a set of observed data about n variables or properties. One problem with estimating one single probability space is the exponential number of events. Approximation is one approach to addressing the problem of the exponential order of the number of events. Alternatively to approximation, we change paradigm - from classical, set-based probability spaces based on sets to quantum probability spaces based on vector subspaces. By changing paradigm, we leverage quantum probability and present an efficient algorithm to calculate a Quantum Probability Space (QPS) in only O(n4) steps.
This paper explores the potential of quantum machine learning (QML) for efficient and accurate probabilistic model learning. Traditional machine learning algorithms often struggle with computational complexity and scalability, particularly when dealing with high-dimensional data and complex probability distributions. This research proposes a novel approach leveraging principles from quantum information theory to design a QML algorithm capable of learning probabilistic models. The core mechanism involves representing model parameters as quantum states and utilizing quantum measurements and entanglement to perform parameter estimation. We aim to demonstrate that this quantum-based method can overcome limitations inherent in classical approaches, potentially leading to significant improvements in both computational efficiency and predictive accuracy. This work presents a foundational framework for further research and development in this emerging field.
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 information theory offers unprecedented opportunities for computational advancement, particularly in the realm of quantum computing. However, the inherent complexity of quantum systems necessitates sophisticated computational techniques. This paper explores the optimization of probabilistic space operations within quantum information theory, a critical aspect for enhancing computation efficiency and achieving more precise results. We introduce a novel optimization framework that leverages the unique properties of probability spaces, leading to algorithmic improvements and enhanced performance. The core mechanism focuses on dynamically adjusting parameters within the probability space to minimize error and maximize fidelity. This research addresses a long-standing challenge in quantum information processing, offering a pathway towards more robust and scalable quantum algorithms.
As ultracold atom experiments become highly controlled and scalable quantum simulators, they require sophisticated control over high-dimensional parameter spaces and generate increasingly complex measurement data that need to be analyzed and interpreted efficiently. Machine learning (ML) techniques have been established as versatile tools for addressing these challenges, offering strategies for data interpretation, experimental control, and theoretical modeling. In this review, we provide a perspective on how machine learning is being applied across various aspects of quantum simulation, with a focus on cold atomic systems. Emphasis is placed on practical use cases -- from classifying many-body phases to optimizing experimental protocols and representing quantum states -- highlighting the specific contexts in which different ML approaches prove effective. Rather than presenting algorithmic details, we focus on the physical insights enabled by ML and the kinds of problems in quantum simulation where these methods offer tangible benefits.
A probability space contains a set of outcomes, a collection of events formed by subsets of the set of outcomes and probabilities defined for all events. A reformulation in terms of propositions allows to use the maximum entropy method to assign the probabilities taking some constraints into account. The construction of a probability space for quantum models is determined by the choice of propositions, choosing the constraints and making the probability assignment by the maximum entropy method. This approach shows, how typical quantum distributions such as Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein are partly related with well-known classical distributions. The relation between the conditional probability density, given some averages as constraints and the appropriate ensemble is elucidated.