Conventional risk analysis and assessment tools rely on the use of probability to represent and quantify uncertainties. Modeling complex engineering problems with pure probabilistic approach can encounter challenges, particularly in cases where contextual knowledge and information are needed to define probability distributions or models. For the study and assessment of risks associated with complex engineering systems, researchers have been exploring augmentation of pure probabilistic techniques with alternative, non-fully, or imprecise probabilistic techniques to represent uncertainties. This exploratory research applies an alternative probability theory, quantum probability and the associated tools of quantum mechanics, to investigate their usefulness as a risk analysis and assessment tool for engineering problems. In particular, we investigate the application of the quantum framework to study complex engineering systems where the tracking of states and contextual knowledge can be a challenge. This study attempts to gain insights into the treatment of uncertainty, to explore the theoretical implication of an integrated framework for the treatment of aleatory and epistemic uncertainties, and to evaluate the use of quantum probability to improve the fidelity and robustness of risk system models and risk analysis techniques.
Conventional risk analysis and assessment tools rely on the use of probability to represent and quantify uncertainties. Modeling complex engineering problems with pure probabilistic approach can encounter challenges, particularly in cases where contextual knowledge and information are needed to define probability distributions or models. For the study and assessment of risks associated with complex engineering systems, researchers have been exploring augmentation of pure probabilistic techniques with alternative, non-fully, or imprecise probabilistic techniques to represent uncertainties. This exploratory research applies an alternative probability theory, quantum probability and the associated tools of quantum mechanics, to investigate their usefulness as a risk analysis and assessment tool for engineering problems. In particular, we investigate the application of the quantum framework to study complex engineering systems where the tracking of states and contextual knowledge can be a challenge. This study attempts to gain insights into the treatment of uncertainty, to explore the theoretical implication of an integrated framework for the treatment of aleatory and epistemic uncertainties, and to evaluate the use of quantum probability to improve the fidelity and robustness of risk system models and risk analysis techniques.
Quantum-enhanced uncertainty quantification (QEQ) offers a paradigm shift in quantifying uncertainty in complex systems, surpassing classical methods' limitations. This paper explores the application of quantum computing to this field, focusing on the development of a novel algorithm for probabilistic distribution estimation. We argue that quantum algorithms can provide a fundamentally more accurate and robust representation of system behavior, leading to improved risk assessment and decision-making in critical applications. The core mechanism centers around leveraging quantum phenomena to enhance the computational complexity of probability distribution estimation, resulting in significantly improved precision and speed. This work presents a preliminary framework demonstrating the potential of quantum computing to revolutionize uncertainty quantification.
Uncertainty in economics still poses some fundamental problems illustrated, e.g., by the Allais and Ellsberg paradoxes.To overcome these difficulties, economists have introduced an interesting distinction between risk and ambiguity depending on the existence of a (classical Kolmogorovian) probabilistic structure modeling these uncertainty situations.On the other hand, evidence of everyday life suggests that context plays a fundamental role in human decisions under uncertainty.Moreover, it is well known from physics that any probabilistic structure modeling contextual interactions between entities structurally needs a non-Kolmogorovian quantum-like framework.In this paper we introduce the notion of contextual risk with the aim of modeling a substantial part of the situations in which usually only ambiguity is present.More precisely, we firstly introduce the essentials of an operational formalism called the hidden measurement approach in which probability is introduced as a consequence of fluctuations in the interaction between entities and contexts.Within the hidden measurement approach we propose a sphere model as a mathematical tool for situations in which contextual risk occurs.We show that a probabilistic model of this kind is necessarily non-Kolmogorovian, hence it requires either the formalism of quantum mechanics or a generalization of it.This insight is relevant, for it explains the presence of quantum or, better, quantum-like, structures in economics, as suggested by some authors, and can serve to solve the aforementioned paradoxes.
Operational demands in industries, such as the energy sector, underscore the critical need for reliable equipment capable of withstanding long-term planning and unpredictable factors.Reliability assessment is important for maintaining productivity and optimizing maintenance strategies, especially in scenarios where data limitations challenge traditional assessment methods.In this context, Bayesian inference has emerged as a dynamic tool to update reliability estimates using data from various hierarchical levels.However, conventional simulation techniques may lack computational efficiency when dealing with the reliability estimation of complex systems, creating opportunities to explore alternative approaches such as quantum computation techniques.Quantum Computing leverages principles of quantum mechanics, such as superposition and entanglement, to try to address these computational challenges more effectively.Previous works have applied quantum Bayesian networks using amplitude amplification methods to the context of risk and reliability, focusing on nodes representing discrete probability distributions.This research aims to enhance this approach by incorporating continuous marginal and conditional probabilities into the analysis, which is particularly relevant for systems that rely on these distributions to model events.We explore the encoding of continuous probability distributions within the amplitude amplification framework, aiming to improve the efficiency and precision of probabilistic inference.Additionally, we apply this methodology to Bayesian networks, benchmarking the performance of quantum methods against classical simulation techniques like Monte Carlo to identify scenarios where quantum techniques demonstrate clear advantages.
Uncertainty in economics still poses some fundamental problems illustrated, e.g., by the Allais and Ellsberg paradoxes. To overcome these difficulties, economists have introduced an interesting distinction between 'risk' and 'ambiguity' depending on the existence of a (classical Kolmogorovian) probabilistic structure modeling these uncertainty situations. On the other hand, evidence of everyday life suggests that 'context' plays a fundamental role in human decisions under uncertainty. Moreover, it is well known from physics that any probabilistic structure modeling contextual interactions between entities structurally needs a non-Kolmogorovian quantum-like framework. In this paper we introduce the notion of 'contextual risk' with the aim of modeling a substantial part of the situations in which usually only 'ambiguity' is present. More precisely, we firstly introduce the essentials of an operational formalism called 'the hidden measurement approach' in which probability is introduced as a consequence of fluctuations in the interaction between entities and contexts. Within the hidden measurement approach we propose a 'sphere model' as a mathematical tool for situations in which contextual risk occurs. We show that a probabilistic model of this kind is necessarily non-Kolmogorovian, hence it requires either the formalism of quantum mechanics or a generalization of it. This insight is relevant, for it explains the presence of quantum or, better, quantum-like, structures in economics, as suggested by some authors, and can serve to solve the aforementioned paradoxes.
This paper introduces a novel approach to modeling non-deterministic systems leveraging the principles of quantum probabilistic reasoning. Traditional methods relying on probabilistic statistical models often struggle with the complexities inherent in high-dimensional and intricate uncertainty. This work proposes a framework that represents system uncertainties as quantum probability distributions, employs quantum probabilistic inference algorithms for information fusion and decision-making, and utilizes quantum interference to optimize the updating process of these distributions. The core claim centers around utilizing the unique characteristics of quantum probabilistic reasoning to design a robust system modeling technique. The proposed mechanism fundamentally shifts the paradigm by incorporating quantum phenomena to enhance accuracy and efficiency in handling non-deterministic scenarios. This approach offers a promising alternative for tackling complex systems where classical probabilistic methods fall short. ---
Interpretational paradoxes of quantum mechanics may be associated with the application of the structure of classical probability theory to systems whose probabilistic organization is fundamentally contextual. In this work, we propose an outline of an alternative probability theory in which the primary object is not an elementary outcome but a contextual whole—a class of alternatives defined by a common structural property. In this approach, probability is organized on two levels. The first level describes the probabilities of contextual wholes, while the second level describes the conditional probabilities of alternatives within those wholes. Individual alternatives do not possess autonomous probabilities outside their context. Their probabilities arise only as contextual projections of a more fundamental probabilistic structure. Within this model, quantum mechanics appears as a special case of a more general theory in which contextual wholes are described by superpositions of probability amplitudes. Classical probability theory emerges as a limiting case in which all contexts are mutually compatible and can be combined into a single global description. The proposed framework provides a possible conceptual foundation for understanding quantum probability, contextuality, interference, and hybrid probability distributions within a unified structure.