Related papers: A Quaternion Frequency and Phasor Estimator for Th…
Here we revisit the quantum phase estimation (QPE) algorithm, and devise an iterative method to improve the precision of QPE with propagators over a variety of time spans. For a given propagator and a certain eigenstate as input, QPE with…
Implementing state estimation in low and medium voltage power distribution is still challenging given the scale of many networks and the reliance of traditional methods on a large number of measurements. This paper proposes a method to…
This paper describes the passage of light through a system of waveplates mathematically in terms of quaternions, an extension of the complex numbers, instead of the more usual Jones vectors and Jones matrices. Both the light beam and the…
The Kalman filter is the most powerful tool for estimation of the states of a linear Gaussian system. In addition, using this method, an expectation maximization algorithm can be used to estimate the parameters of the model. However, this…
We present efficient circuits that can be used for the phase space tomography of quantum states. The circuits evaluate individual values or selected averages of the Wigner, Kirkwood and Husimi distributions. These quantum gate arrays can be…
This article considers the problem of designing adaption and optimisation techniques for training quantum learning machines. To this end, the division algebra of quaternions is used to derive an effective model for representing computation…
Accurate state estimates are required for increasingly complex systems, to enable, for example, feedback control. However, available state estimation schemes are not necessarily real-time feasible for certain large-scale systems. Therefore,…
Topological phase classifications have been intensively studied via machine-learning techniques where different forms of the training data are proposed in order to maximize the information extracted from the systems of interests. Due to the…
This document describes standard approaches for filtering and estimation for quadrotors, created for the Udacity Flying Cars course. We assume previous knowledge of probability and some knowledge of linear algebra. We do not assume previous…
The problem of effective use of Phasor Measurement Units (PMUs) to enhance power systems awareness and security is a topic of key interest. The central question to solve is how to use this new measurements to reconstruct the state of the…
An optimal estimator of quantum states based on a modified Kalman's Filter is proposed in this work. Such estimator acts after state measurement, allowing obtain an optimal estimation of quantum state resulting in the output of any quantum…
Quantum phase estimation is a core task in quantum technologies ranging from metrology to quantum computing, where it appears as a key subroutine in various algorithms. Here, we quantitatively connect the performance of phase estimation…
Quaternion, an extension of complex number, is the first discovered non-commutative division algebra by William Rowan Hamilton in 1843. In this article, we review the recent progress on building up the connection between the mathematical…
Modern power systems are at risk of largely reducing the inertia of generation assets and prone to experience extreme dynamics. The consequence is that, during electromechanical transients triggered by large contingencies, transmission of…
Numerous attempts have been made to replicate the success of complex-valued algebra in engineering and science to other hypercomplex domains such as quaternions, tessarines, biquaternions, and octonions. Perhaps, none have matched the…
Quantum algorithms for diverse problems, including search and optimization problems, require the implementation of a reflection operator over a target state. Commonly, such reflections are approximately implemented using phase estimation.…
In recent years, several models using Quaternion-Valued Convolutional Neural Networks (QCNNs) for different problems have been proposed. Although the definition of the quaternion convolution layer is the same, there are different…
The problem of imbalance detection in a three-phase power system using a phasor measurement unit (PMU) is considered. A general model for the zero, positive, and negative sequences from a PMU measurement at off-nominal frequencies is…
We present a general nonlinear Bayesian filter for high-dimensional state estimation using the theory of reproducing kernel Hilbert space (RKHS). Applying kernel method and the representer theorem to perform linear quadratic estimation in a…
Quaternion-valued wireless communication systems have been studied in the past. Although progress has been made in this promising area, a crucial missing link is lack of effective and efficient quaternion-valued signal processing algorithms…