Quantum Mechanical Phenomena Research Articles

Quantum Mechanics and Classical Optics: New Ways to Combine Classical and Quantum Methods

Quantum Mechanics and classical optics feature similar phenomena such as superposition, interference and even entanglement. Hence, techniques from optics can be used in quantum mechanics and vice versa. In this article I address the question: What can we learn from formulating optics in the language of quantum mechanics? It is argued that the solutions of the wave equations for the electromagnetic field form a tensor product of Hilbert spaces corresponding to the degrees of freedom of classical light. Therefore, it comprises non-separable solutions reminiscent of entanglement. Moreover, the two spatial degrees of freedom each carry non-commuting position and momentum variables forming a Heisenberg algebra like quantum particles moving in a two dimensional space. An analogy between the dynamics of a quantum harmonic oscillator and paraxial light propagating through a converging lens is drawn. This article presents a modern formulation of optics in the language of state vectors and operators (based on Dirac’s notation) along the lines of an earlier contribution [1], specifying and explaining its results.

Solution of Laguerre’s Differential Equations via Modified Adomian Decomposition Method

This paper presents a technique for obtaining an exact solution for the well-known Laguerre’s differential equations that arise in the modeling of several phenomena in quantum mechanics and engineering. We utilize an efficient procedure based on the modified Adomian decomposition method to obtain closed-form solutions of the Laguerre’s and the associated Laguerre’s differential equations. The proposed technique makes sense as the attitudes of the acquired solutions towards the neighboring singular points are correctly taken care of.

Fission studies in inverse kinematics with the R3B setup

Nuclear fission is a complex dynamical process, whose description involves the coupling between intrinsic and collective degrees of freedom, as well as different quantum-mechanical phenomena. For this reason, to this day it still lacks a satisfactory and complete microscopic description. In addition to the importance of describing fission itself, studies of the r-process in astrophysics depend on fission observables to constrain the theoretical models that explain the isotopic abundances in the Universe. To improve on the existing data, fission reactions of heavy nuclei in inverse kinematics are produced in quasi-free (p,2p) scattering reactions, which induce fission through particle-hole excitations that can range from few to tens of MeV. In order to study the evolution of the fission yields with temperature, the excitation energy of the fissioning system must be reconstructed, which is possible by measuring the four-momenta of the two outgoing protons. Performing this kind of experiment requires a complex experimental setup, providing full isotopic identification of both fission fragments and an accurate measurement of the momenta of the two outgoing protons. This was realized recently at the GSI/FAIR facility and some of the results obtained for the charge distributions are presented in this work.

Mass-Oscillators as Information Memories of Action

In the theory of physical information, the physical phenomena of electromagnetism, quantum mechanics and gravity can be described by means of the action as information enclosed in four dimensional structures with oscillator properties, under the conditions of the Hamilton principle. The present report shows that it is also possible to simulate the behaviour of the mass under these conditions. As a result, among other things, the statements are obtained that the mass is stored virtual action; the rest frame of elementary objects and the inertia of matter are caused by the action stored in the mass oscillators.

Solvability of a nonlinear integro-differential equation with fractional order using the Bernoulli matrix approach

<abstract> <p>Under some suitable conditions, we study the existence and uniqueness of a solution to a new modification of a nonlinear fractional integro-differential equation (<bold>NFIDEq</bold>) in dual Banach space C<sub>E</sub> (E, [0, T]), which simulates several phenomena in mathematical physics, quantum mechanics, and other domains. The desired conclusions are demonstrated with the use of fixed-point theorems after applying the theory of fractional calculus. The validation of the provided strategy has been done by utilizing the Bernoulli matrix approach (<bold>BMA</bold>) method as a numerical method. The major motivation for selecting the <bold>BMA</bold> approach is that it combines Bernoulli polynomial approximation with Caputo fractional derivatives and numerical integral transformation to reduce the <bold>NFIDEq</bold> to an algebraic system and then derive the numerical solution; additionally, the convergence analysis indicated that the proposed strategy has more precision than other numerical methods. Finally, as a verification of the theoretical work, we apply two examples with numerical results by using [Matlab R2022b], illustrating the comparisons between the exact solutions and numerical solutions, as well as the absolute error in each case is computed.</p> </abstract>

Hybrid Quantum-Classical Generative Adversarial Network for synthesizing chemically feasible molecules

Current drug discovery processes can cost billions of dollars and usually take five to ten years. People have been researching and implementing various computational approaches to search for molecules and compounds from the chemical space, which can be on the order of 1060 molecules. One solution involves deep generative models, which are artificial intelligence models that learn from nonlinear data by modeling the probability distribution of chemical structures and creating similar data points from the trends it identifies. These generative models can extract salient features that characterize the molecules. However, they often suffer from increased time complexity. Aiming for faster runtime and greater robustness when analyzing high-dimensional data, we designed and implemented a Hybrid Quantum-Classical Generative Adversarial Network (QGAN) to synthesize molecules. There are two parts in the QGAN: a quantum generator that creates molecules based on the probability distributions of likely combinations and a classical discriminator that differentiates real molecules from the generated ones. We hypothesized that a quantum generator would be more impactful, offering a runtime speedup and increasing generated molecule possibilities, because we could use quantum mechanical phenomena superposition, entanglement, and interference to analyze more atom-bond combinations than a classical generator. The PyTorch-PennyLane implementation of the QGAN generated seven chemically stable molecules out of 300, a 2.3% success rate. Although the QGAN is a work in progress, it has demonstrated a path towards more efficient drug development, which would accelerate the development of medicines and reduce costs for the whole R&D process.

The Effect of the Number of Entangled Photons on the Number of Coincidences Rate, Bell’s Inequality and the Error Rate by the Delphi Program

Quantum cryptography is a science that relies on the use of a protocol designed to exploit quantum mechanical phenomena to achieve the secrecy of cryptographic keys. This work aimed to generate a quantum key based on polarization-entangled photon pairs; to eliminate the error by implementing the BB89 protocol using the Delphi language program in order to obtain a high degree of security. The results explain the effect of the number of EPR photons pair running from (500-10000) photons on the number of coincidences, expected error and Bell's parameter discussed as; Total coincidences of the Bell – CHSH increases with increasing of EPR pairs, and values were stable when EPR pairs were increased, there was a small random change in the expected error rate (in case of no eavesdropping).This study concludes thatTotal coincidences of the Bell and expected error are affected by the number of entangled photons.The increasing of the length of key must increase the number of EPR and decrease the Error and Bell's value must be stable.

The World in the Wave Function

<i>The World in the Wave Function</i>

Novel Quantum Sensors for Light Dark Matter and Neutrino Detection

The fields of light dark matter and neutrino physics offer compelling signals at recoil energies of eV to even meV, well below the [Formula: see text] keV thresholds of many techniques currently employed in these fields. Sensing of such small energies can benefit from the emergence of so-called quantum sensors, which employ fundamentally quantum mechanical phenomena to transduce energy depositions into electrical signals. This review focuses on quantum sensors under development that will enhance and extend the search for “particle-like” interactions of dark matter or enable new measurements of neutrino properties in the coming years.

Power and Energy Applications Based on Quantum Computing: The Possible Potentials of Grover’s Algorithm

In quantum computing, calculations are achieved using quantum mechanics. Typically, two main phenomena of quantum mechanics (i.e., superposition and entanglement) allow quantum computing to solve some problems more efficiently than classical algorithms. The most well-known advantage of quantum computing is the speedup of some of the calculations, which have been performed before by classical applications. Scientists and engineers are attempting to use quantum computing in different fields of science, e.g., drug discovery, chemistry, computer science, etc. However, there are few attempts to use quantum computing in power and energy applications. This paper tries to highlight this gap by discussing one of the most famous quantum computing algorithms (i.e., Grover’s algorithm) and discussing the potential applications of this algorithm in power and energy systems, which can serve as one of the starting points for using Grover’s algorithm in power and energy systems.

Multiclass Classification of Metrologically Resourceful Tripartite Quantum States with Deep Neural Networks.

Quantum entanglement is a unique phenomenon of quantum mechanics, which has no classical counterpart and gives quantum systems their advantage in computing, communication, sensing, and metrology. In quantum sensing and metrology, utilizing an entangled probe state enhances the achievable precision more than its classical counterpart. Noise in the probe state preparation step can cause the system to output unentangled states, which might not be resourceful. Hence, an effective method for the detection and classification of tripartite entanglement is required at that step. However, current mathematical methods cannot robustly classify multiclass entanglement in tripartite quantum systems, especially in the case of mixed states. In this paper, we explore the utility of artificial neural networks for classifying the entanglement of tripartite quantum states into fully separable, biseparable, and fully entangled states. We employed Bell’s inequality for the dataset of tripartite quantum states and train the deep neural network for multiclass classification. This entanglement classification method is computationally efficient due to using a small number of measurements. At the same time, it also maintains generalization by covering a large Hilbert space of tripartite quantum states.

Klein tunneling for Lamb waves in elastic phononic crystal plates

Klein tunneling is an intriguing phenomenon in quantum mechanics, which refers to the unity transmission of particles through a higher energy barrier without hindrance in the case of normal incidence. The introduction of phononic crystals enables the direct observation of this phenomenon from a different point, giving rise to a broader application prospect. In this paper, we aim at realizing the Klein tunneling for elastic plate waves. To this end, we combine two kinds of Y-shaped phononic crystals with different Dirac point energies to structure a sandwich-like plate, which supports the propagation of Lamb waves while artificially introducing a potential barrier. Under such a configuration, perfect wave transmission regardless of the barrier in a wide frequency range can be realized, which also enables the numerical prediction and experimental observation of the Klein tunneling phenomenon in Lamb waves. The results of this work provide a direction and reference for the design and applications of phononic crystal devices, such as the chip-scale elastic waveguides.

Neutron waveguides with finite repulsive potential in clad

The interaction of an incoming slow neutron with a straight semi-infinite material waveguide (physically, a very lengthy one) located in vacuum (clad) in the infinite three-dimensional (3D) space is studied. The waveguide creates an attractive potential on the neutron. The physical quantum-mechanical wave phenomena are: (i) reflection and scattering of the neutron by the waveguide and (ii) its confined propagation along the latter, in specific propagation modes. The direct application of standard scattering integral equations meets several difficulties, arising mainly from the infinite length of the waveguide and (ii). New and more convenient 3D scattering integral equations are proposed and discussed, using suitable Green functions, adequate for the semi-infinite waveguide and accounting for (i) and the above difficulties. Approximate formulae for the probability amplitudes and fluxes for (i) and (ii) are given: in particular, the formulas for slow neutron confined propagation extend the ones given previously for optical waveguides. Some detailed applications and numerical computations for two-dimensional media and waveguides are presented.

A Model of Anaphoric Ambiguities using Sheaf Theoretic Quantum-like Contextuality and BERT

Ambiguities of natural language do not preclude us from using it and context helps in getting ideas across. They, nonetheless, pose a key challenge to the development of competent machines to understand natural language and use it as humans do. Contextuality is an unparalleled phenomenon in quantum mechanics, where different mathematical formalisms have been put forwards to understand and reason about it. In this paper, we construct a schema for anaphoric ambiguities that exhibits quantum-like contextuality. We use a recently developed criterion of sheaf-theoretic contextuality that is applicable to signalling models. We then take advantage of the neural word embedding engine BERT to instantiate the schema to natural language examples and extract probability distributions for the instances. As a result, plenty of sheaf-contextual examples were discovered in the natural language corpora BERT utilises. Our hope is that these examples will pave the way for future research and for finding ways to extend applications of quantum computing to natural language processing.

Quantized current steps due to the a.c. coherent quantum phase-slip effect.

The a.c. Josephson effect predicted in 19621 and observed experimentally in 19632 as quantized 'voltage steps' (the Shapiro steps) from photon-assisted tunnelling of Cooper pairs is among the most fundamental phenomena of quantum mechanics and is vital for metrological quantum voltage standards. The physically dual effect, the a.c. coherent quantum phase slip (CQPS), photon-assisted tunnelling of magnetic fluxes through a superconducting nanowire, is envisaged to reveal itself as quantized 'current steps'3,4. The basic physical significance of the a.c. CQPS is also complemented by practical importance in future current standards, a missing element for closing the quantum metrology triangle5,6. In 2012, the CQPS was demonstrated as superposition of magnetic flux quanta in superconducting nanowires 7. However, the direct flat current steps in superconductors, the only unavailable basic effect of superconductivity to date, was unattainable due to lack of appropriate materials and challenges in circuit engineering. Here we report the direct observation of the dual Shapiro steps in a superconducting nanowire. The sharp steps are clear up to 26 GHz frequency with current values 8.3 nA and limited by the present set-up bandwidth. The current steps were theoretically predicted in small Josephson junctions 30 years ago5. However, unavoidable broadening in Josephson junctions prevents their direct experimental observation8,9. We solve this problem by placing a thin NbN nanowire in an inductive environment.

Scalable Method for Eliminating Residual ZZ Interaction between Superconducting Qubits.

Unwanted ZZ interaction is a quantum-mechanical crosstalk phenomenon which correlates qubit dynamics and is ubiquitous in superconducting qubit systems. It adversely affects the quality of quantum operations and can be detrimental in scalable quantum information processing. Here we propose and experimentally demonstrate a practically extensible approach for complete cancellation of residual ZZ interaction between fixed-frequency transmon qubits, which are known for long coherence and simple control. We apply to the intermediate coupler that connects the qubits a weak microwave drive at a properly chosen frequency in order to noninvasively induce an ac Stark shift for ZZ cancellation. We verify the cancellation performance by measuring vanishing two-qubit entangling phases and ZZ correlations. In addition, we implement a randomized benchmarking experiment to extract the idling gate fidelity which shows good agreement with the coherence limit, demonstrating the effectiveness of ZZ cancellation. Our method allows independent addressability of each qubit-qubit connection and is applicable to both nontunable and tunable couplers, promising better compatibility with future large-scale quantum processors.

Klein-Like Tunneling of Sound via Negative Index Metamaterials

Klein tunneling is a counterintuitive quantum-mechanical phenomenon, predicting perfect transmission of relativistic particles through higher-energy barriers. This phenomenon was shown to be supported at normal incidence in graphene due to pseudospin conservation. Here I show that Klein-tunneling analogy can occur in classical systems, and remarkably, does not rely on mimicking graphene's spinor wave-function structure. Instead, the mechanism requires a particular form of constitutive parameters of the penetrated medium, yielding transmission properties identical to the quantum tunneling in graphene. I demonstrate this result by simulating tunneling of sound in a two-dimensional acoustic metamaterial. More strikingly, I show that by introducing a certain form of anisotropy, the tunneling can be made unimpeded for any incidence angle, while keeping most of its original Klein dispersion properties. This phenomenon may be denoted by the omnidirectional Klein-like tunneling. The suggested tunneling mechanism and its omnidirectional variant may be useful for applications requiring lossless and direction-independent transmission of classical waves.

Developing a Model for Predicting Lung Cancer Using Variational Quantum-Classical Algorithm: A Survey

There are real life problems that currently proved hard for classical computers (even the best of supercomputers) to solve-the so called computationally intractable problems. Computers and computing devices are limited, by virtue of the fact that they cannot perform certain complex problems. For example, modern cryptography assumes that it is impossible to factorize a large number as the complexity of solving this problem increases exponentially. Even the best supercomputers of today cannot sufficiently find the prime factors of a number with 700-1,000 digits. With quantum computing, however, Shor’s algorithm proved that in principle, a quantum computer can be used to break the security of conventional cryptosystems. Quantum computing also promises exponential improvements for many optimization problems. Lov Grover algorithm was also designed to search for an element in unstructured database. Effort is currently on to leverage quantum computing and quantum mechanical phenomena to tackle complex machine learning problems. Using machine learning algorithm to solve problems is common place. What is however new is using quantum machine learning algorithm to solve problems such as detecting, classifying and predicting disease such as lung cancer. In this work, we highlight the limitations of classical computers to solve certain problems and then propose a hybrid model called the variational quantum-classical algorithm to predict the possibility of a patient developing lung cancer given a set of features which are spelt out in the dataset. The dataset is initially pre-processed, and made to pass through a Parameterized Quantum Circuit (PQC) and then post-processed. Finally, the output of the post-processing phase is used for prediction of lung cancer.

The wave function as a true ensemble.

In quantum mechanics, the wave function predicts probabilities of possible measurement outcomes, but not which individual outcome is realized in each run of an experiment. This suggests that it describes an ensemble of states with different values of a hidden variable. Here, we analyse this idea with reference to currently known theorems and experiments. We argue that the ψ-ontic/epistemic distinction fails to properly identify ensemble interpretations and propose a more useful definition. We then show that all local ψ-ensemble interpretations which reproduce quantum mechanics violate statistical independence. Theories with this property are commonly referred to as superdeterministic or retrocausal. Finally, we explain how this interpretation helps make sense of some otherwise puzzling phenomena in quantum mechanics, such as the delayed choice experiment, the Elitzur–Vaidman bomb detector and the extended Wigner’s friends scenario.

Heteronuclear soliton molecules with two frequencies

Bound states of optical solitons represent ideal candidates to investigate fundamental nonlinear wave interaction principles and have been shown to exhibit intriguing analogies to phenomena in quantum mechanics. Usually, such soliton molecules are created by a suitable balance of phase-related attraction and repulsion between two copropagating solitons with overlapping tails. However, there exists also another type of compound state, where strong binding forces result directly from the Kerr nonlinearity between solitons at different center frequencies. The physical mechanisms as well as the properties of these objects are quite different from those of usual soliton molecules, but are hardly known. Here we characterize and investigate these compound states in greater detail. We demonstrate unique propagation dynamics by investigating the robustness of the compound states under perturbations, such as third-order dispersion and the Raman effect. The constituents are individually affected by the perturbations, but the impact on the compound state is not a mere superimposition. One observes complex dynamics resulting from a strong entanglement between the subpulses. For example, in the case of the Raman effect both subpulses are subject to a cancellation of the self-frequency shift, although only one subpulse is approaching a zero-dispersion frequency. We extend the concept of the molecule states to three and more constituents by adopting appropriate propagation constants. These multicolor soliton molecules open up further perspectives for exploring the complex physics of photonic molecules, but also show great potential for application resulting from their robustness and the possibility to control their properties.