Jyoti Rani

Dominic Widdows, Jyoti Rani, Emmanuel Pothos

This paper demonstrates that some non-classical models of human decision-making can be run successfully as circuits on quantum computers. Since the 1960s, many observed cognitive behaviors have been shown to violate rules based on classical probability and set theory. For example, the order in which questions are posed in a survey affects whether participants answer 'yes' or 'no', so the population that answers 'yes' to both questions cannot be modeled as the intersection of two fixed sets. It can, however, be modeled as a sequence of projections carried out in different orders. This and other examples have been described successfully using quantum probability, which relies on comparing angles between subspaces rather than volumes between subsets. Now in the early 2020s, quantum computers have reached the point where some of these quantum cognitive models can be implemented and investigated on quantum hardware, by representing the mental states in qubit registers, and the cognitive operations and decisions using different gates and measurements. This paper develops such quantum circuit representations for quantum cognitive models, focusing particularly on modeling order effects and decision-making under uncertainty. The claim is not that the human brain uses qubits and quantum circuits explicitly (just like the use of Boolean set theory does not require the brain to be using classical bits), but that the mathematics shared between quantum cognition and quantum computing motivates the exploration of quantum computers for cognition modeling. Key quantum properties include superposition, entanglement, and collapse, as these mathematical elements provide a common language between cognitive models, quantum hardware, and circuit implementations.

Jyoti Rani, Tapas Tripura, Hariprasad Kodamana et al.

Fault detection and isolation in complex systems are critical to ensure reliable and efficient operation. However, traditional fault detection methods often struggle with issues such as nonlinearity and multivariate characteristics of the time series variables. This article proposes a generative adversarial wavelet neural operator (GAWNO) as a novel unsupervised deep learning approach for fault detection and isolation of multivariate time series processes.The GAWNO combines the strengths of wavelet neural operators and generative adversarial networks (GANs) to effectively capture both the temporal distributions and the spatial dependencies among different variables of an underlying system. The approach of fault detection and isolation using GAWNO consists of two main stages. In the first stage, the GAWNO is trained on a dataset of normal operating conditions to learn the underlying data distribution. In the second stage, a reconstruction error-based threshold approach using the trained GAWNO is employed to detect and isolate faults based on the discrepancy values. We validate the proposed approach using the Tennessee Eastman Process (TEP) dataset and Avedore wastewater treatment plant (WWTP) and N2O emissions named as WWTPN2O datasets. Overall, we showcase that the idea of harnessing the power of wavelet analysis, neural operators, and generative models in a single framework to detect and isolate faults has shown promising results compared to various well-established baselines in the literature.