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Informatics and Scientific Computing approach parallel processing in a different way. We briefly describe the different points of view of both camps. Next we concentrate on a case study in the area of scientific computing. The problem chosen is from Physical Chemistry (self-consistent field computation). We describe the problem, the sequential solution, the parallelization strategy and present the performance values we have achieved. Our implementation is based on a 60-node transputer system, available at the Parallel Processing Laboratory in Basel.

Using a recent construction of observables characterizing the time of occurence of an effect in quantum theory, we present a rigorous derivation of the standard time-energy uncertainty relation. In addition, we prove an uncertainty relation for time measurements alone.

We present a suitable framework for the definition of quantum time delay in terms of sojourn times for unitary operators in a two-Hilbert spaces setting. We prove that this time delay defined in terms of sojourn times (time-dependent definition) exists and coincides with the expectation value of a unitary analogue of the Eisenbud–Wigner time delay operator (time-independent definition). Our proofs rely on a new summation formula relating localization operators to time operators and on various tools from functional analysis such as Mackey’s imprimitivity theorem, Trotter–Kato formula and commutator methods for unitary operators. Our approach is general and model-independent.

We study Feynman checkers, the most elementary model of electron motion introduced by  Feynman. For the model, we prove that the probability to find an electron vanishes nowhere inside the light cone. We also prove several results on the average electron velocity. In addition, we present a lot of identities related to the model.

We study the adiabatic limit for Hamiltonians with certain complex-analytic dependence on the time variable We show that the transition probability from a spectral band that is separated by gaps is exponentially small in the adiabatic parameter We find sufficient conditions for the Landau-Zener formula, and its generalization to nondiscrete spectrum, to bound the transition probability

The ability to simulate several aspects of two-dimensional quantum mechanics is discussed, in conjunction with an ongoing visualization project, WebTOP, that has been of recognizable importance to physics education since its inception in the late 1990s. In the past, the WebTOP project has been primarily used as a means of visualizing optics and wave phenomena and, now, the development of certain interactive quantum mechanical demonstrations has the potential to strengthen its power as an educational tool for the physics community. The added functionality for propagating wave packets forward in time for a given 2D potential gives rise to the ability to investigate interesting quantum behaviors. Fractional revivals of states in the 2D infinite square well can be clearly seen as well as the time delay of scattered wave packets for certain step potentials. Aspects of squeezed and coherent states of the 2D harmonic oscillator potential can also be explored, among other observable phenomena.

We implement in a reactive programming framework a system mimicking three aspects of quantum mechanics: self-interference, state superposition, and entanglement. The system basically consists in a cellular automaton embedded in a synchronous environment which defines global discrete instants and broadcast events. The implementation shows how a simulation of fundamental aspects of quantum mechanics can be obtained from the synchronous parallel combination of a small number of elementary components.

The modified Schrödinger equation obtained by Costa Filho et al. [Phys. Rev. A84, 050102(R) (2011)] is shown to be a Sturm–Liouville problem. This demonstration guarantees that Hamiltonian eigenvalues obtained in this formalism are real. It also allows us to show that, regardless of the non-Hermitian characteristic of the Hamiltonian operator in the Hilbert space, its time evolution remains unitary.

Taking partial traces (PTrs) for computing reduced density matrices, or related functions, is a ubiquitous procedure in the quantum mechanics of composite systems. In this paper, we present a thorough description of this function and analyze the number of elementary operations (ops) needed, under some possible alternative implementations, to compute it on a classical computer. As we note, it is worthwhile doing some analytical developments in order to avoid making null multiplications and sums, what can considerably reduce the ops. For instance, for a bipartite system ${{\mathscr{H}}}_a\otimes {{\mathscr{H}}}_b$ with dimensions $d_a=dim{{\mathscr{H}}}_a$ and $d_b=dim{{\mathscr{H}}}_b$ and for $d_a,d_b\gg 1$, while a direct use of PTr definition applied to ${{\mathscr{H}}}_b$ requires ${𝒪}(d_a^6{d}_b^6)$ ops, its optimized implementation entails ${𝒪}(d_a^2{d}_b)$ ops. In the sequence, we regard the computation of PTrs for general multipartite systems and describe Fortran code provided to implement it numerically. We also consider the calculation of reduced density matrices via Bloch’s parametrization with generalized Gell Mann’s matrices.

This paper addresses an autonomous facial expression recognition system using the feature selection approach of the Quantum-Inspired Binary Gravitational Search Algorithm (QIBGSA). The detection of facial features completely depends upon the selection of precise features. The concept of QIBGSA is a modified binary version of the gravitational search algorithm by mimicking the properties of quantum mechanics. The QIBGSA approach reduces the computation cost for the initial extracted feature set using the hybrid approach of Local binary patterns with Gabor filter method. The proposed automated system is a sequential system with experimentation on the image-based dataset of Karolinska Directed Emotional Faces (KDEF) containing human faces with seven different emotions and different yaw angles. The experiments are performed to find out the optimal emotions using the feature selection approach of QIBGSA and classification using a deep convolutional neural network for robust and efficient facial expression recognition. Also, the effect of variations in the yaw angle (front to half side view) on facial expression recognition is studied. The results of the proposed system for the KDEF dataset are determined in three different cases of frontal view, half side view, and combined frontal and half side view images. The system efficacy is analyzed in terms of recognition rate.

In recent years, the increasing human–computer interaction has spurred the interest of researchers towards facial expression recognition to determine the expressive changes in human beings. The detection of relevant features that describe the expressions of different individuals is vital to describe human expressions accurately. The present work has employed the integrated concept of Local Binary Pattern and Histogram of Gradient for facial feature extraction. The major contribution of the paper is the optimization of the extracted features using quantum-inspired meta-heuristic algorithms of QGA (Quantum-Inspired Genetic Algorithm), QGSA (Quantum-Inspired Gravitational Search Algorithm), QPSO (Quantum-Inspired Particle Swarm Optimization), and QFA (Quantum-Inspired Firefly Algorithm). These quantum-inspired meta-heuristic algorithms utilize the attributes of quantum computing that ensure the adequate control of facial feature diversity with quantum measures and Q-bit superstition states. The optimized features are fed to the deep learning (DL) variant deep convolutional neural network added with residual blocks (DCNN-R) for the classification of expressions. The facial expressions are detected for the KDEF and RaFD datasets under varying yaw angles of –90^∘, –45^∘, 0^∘, 45^∘, and 90^∘. The detection of facial expressions with varying angles is also a crucial contribution, as the features decrease with the increasing yaw angle movement of the face. The experimental evaluations demonstrate the superior performance of the QFA than other algorithms for feature optimization and hence the better classification of facial expressions.

In this work, we present a simple and efficient method to compute numerically the eigenvalues of complex PT-symmetric Hamiltonian. Numerous works have been devoted to such Hamiltonians since the discovery that they admit totally or partially real spectra. To our knowledge, the method we are advocating has not been used in this context. Besides the determination of real eigenvalues, it allows us to observe the symmetry breaking and to calculate the imaginary parts of the energy.

It is shown that Symbolic Computation provides excellent tools for solving quantum mechanical problems by perturbation theory. The method presented herein solves for both the eigenfunctions and eigenenergies as power series in the order parameter where each coefficient of the perturbation series is obtained in closed form. The algorithms are expressed in the Maple symbolic computation system but can be implemented on other systems. This approach avoids the use of an infinite basis set and some of the complications of degenerate perturbation theory. It is general and can, in principle, be applied to many separable systems.

The synchronization of asynchronous signals can lead to metastable behavior and malfunction of digital circuits. It is believed — but not proved — that metastability principally cannot be avoided. Confusion exists about its practical importance. This paper shows that metastable behavior can be avoided by usage of quantum synchronizers in principle, but not in practice, and that conventional synchronizers unavoidably show metastable behavior in principle, but not in practice, if properly designed.

A molecular dynamics simulation method designed for the analysis of hot electrons-lattice interactions is presented. The physics is based on a simplified quantum mechanical approach and from the computational point of view the simulation has been designed for parallel computing. The results are in agreement with other theories and experimental trends.

A lattice formulation of nonrelativistic quantum mechanics is presented, based on a formal analogy with discrete kinetic theory. The method is applied to the Gross–Pitaevski equation, a specific form of self-interacting nonlinear Schrödinger equation relevant to the study of Bose–Einstein condensation.

Recognizing that syntactic and semantic structures of classical logic are not sufficient to understand the meaning of quantum phenomena, we propose in this paper a new interpretation of quantum mechanics based on evidence theory. The connection between these two theories is obtained through a new language, quantum set theory, built on a suggestion by J. Bell. Further, we give a modal logic interpretation of quantum mechanics and quantum set theory by using Kripke's semantics of modal logic based on the concept of possible worlds. This is grounded on previous work of a number of researchers (Resconi, Klir, Harmanec) who showed how to represent evidence theory and other uncertainty theories in terms of modal logic. Moreover, we also propose a reformulation of the many-worlds interpretation of quantum mechanics in terms of Kripke's semantics. We thus show how three different theories — quantum mechanics, evidence theory, and modal logic — are interrelated. This opens, on one hand, the way to new applications of quantum mechanics within domains different from the traditional ones, and, on the other hand, the possibility of building new generalizations of quantum mechanics itself.

The continuity, equation relating the change in time of the position probability density to the gradient of the probability current density is generalized to PT-symmetric quantum mechanics. The normalization condition of eigenfunctions is modified in accordance with this new conservation law and illustrated with some detailed examples.

The program to construct minimum-uncertainty coherent states for general potentials works transparently with solvable analytic potentials. However, when an analytic potential is not completely solvable, like for a double-well or the linear (gravitational) potential, there can be a conundrum. Motivated by supersymmetry concepts in higher dimensions, we show how these conundrums can be overcome.

We construct two commuting sets of creation and annihilation operators for the PT-symmetric oscillator. We then build coherent states of the latter as eigenstates of such annihilation operators by employing a modified version of the normalization integral that is relevant to PT-symmetric systems. We show that the coherent states are normalizable only in the range (0,1) of the underlying coupling parameter α.