Quantum Concepts Research Articles

Quantum Science and Technologies in K-12: Supporting Teachers to Integrate Quantum in STEM Classrooms

Quantum science and computing represent a vital intersection between science and technology, gaining increasing importance in modern society. There is a pressing need to incorporate these concepts into the K-12 curriculum, equipping new generations with the tools to navigate and thrive in an evolving technological landscape. This study explores the professional learning of K-12 teachers (n = 49) related to quantum concepts and pedagogy. We used open-ended surveys, field notes, workshop artifacts, and interviews to examine teachers’ perceptions of quantum and how they made connections between quantum and their curriculum. Our data reveal that most teachers were excited and interested in teaching quantum but were aware of potential barriers and concerns that might get in the way of teaching quantum. We found that teachers readily identified connections to math and science in their curriculum, but only a few made connections to computing. Enthusiasm for teaching quantum concepts was found in both elementary and secondary educators, suggesting a widespread recognition of its importance in preparing students for a future where quantum technology is a fundamental aspect of their lives and careers.

Mathematical Symbols in Academic Writing: The Case of Incorporating Mathematical Ideals in Academic Writing for Education Researchers

Mathematical symbols, such as those embodying quantum concepts, are indispensable for conveying complex ideas and relationships in academic writing. However, some education researchers and students keep a distance from anything mathematical: algebraic equations, geometrical reasoning, or statistical symbols. How to lower the access threshold for this type of mathematical narrative and reveal the meanings of a range of quantum conceptions to modern educators thus becomes a real problem. Using the pendulum motion equation as a reference point, I argue in this article for the advantages of academic English or French writing genres that fuse a range of mathematical symbols of quantum concepts and conceptual change. Such writings help demonstrate how incorporating the idea of probability (a) refines the debate among conceptual, verbal, and mathematical academic writing; (b) allows new conceptions that draw on the insights from quantum cognition-supported theories; (c) helps explain students’ understanding of mathematical symbols; and (d) offers a new taxonomy for categorizing academic writings.

Archetypal Resonances Between Realms: The Fractal Interplay of Chaos and Order

The intricate balance between chaos and order has fascinated humans for centuries, serving as a recurring theme in culture, psychology, and science. Carl Jung’s insights into archetypes reveal cultural patterns that emerge nearly universally across the globe, independent of history. This paper connects archetypal psychology with contemporary mathematical and quantum concepts. We focus on profound interconnectedness at the interface between chaos and order, by demonstrating how the Mandelbrot set from contemporary fractal geometry circles round to embody the Ouroboros, ancient symbol of recursive dynamics. Our research bridges micro and macro realms, symbolic meanings, and empirical data, as well as psychological and physical dimensions. By merging age-old symbols with cutting-edge mathematical and quantum ideas, we shed light on the intricate dance of chaos and to underscore the unified nature of existence.

Undergraduate students’ models of single- and multi-electron atoms

ABSTRACT Quantum physics forms the basis for exciting new technologies, including quantum computers, quantum encryption, and quantum entanglement. The advancement of science and technology highlights the importance of mastering quantum physics and its applications, not only at the college level but also as early as high school. In this multiple case study, we investigated first- and second-year undergraduate college students’ models of single and multi-electron atoms after completing a modern mechanics course, which addressed basic QM topics. The students’ models were categorised into four primary categories: the discrete entity (particle) model, hybrid model, quantum-like model, and quantum model, and subcategories for atom structure and electron attribution and motion. Despite being introduced to quantum concepts in high school and first-year undergraduate calculus-based physics classes, many students constructed incomplete, inaccurate, or incoherent models. Seven of eight students’ atomic structure models and six of eight students’ electron attribution and motion models were classified as discrete entity and hybrid models. The findings of this study reveal students’ conceptual challenges in explaining the structure of single and multiple-electron atoms and shed light on the factors contributing to the persistent difficulties in their understanding of atomic structure in the realm of quantum mechanics.

QFaaS: A Serverless Function-as-a-Service framework for Quantum computing

Quantum computing is rapidly reaching a point in which its application design and engineering aspects must be seriously considered. However, quantum software engineering is still in its infancy, with numerous challenges, especially in dealing with the diversity of quantum programming languages and noisy intermediate-scale quantum (NISQ) systems. To alleviate these challenges, we propose QFaaS, a holistic Quantum Function-as-a-Service framework, which leverages the advantages of the serverless model, DevOps lifecycle, and the state-of-the-art software techniques to advance practical quantum computing for next-generation application development in the NISQ era. Our framework provides essential elements of a serverless quantum system to streamline service-oriented quantum application development in cloud environments, such as combining hybrid quantum–classical computation, automating the backend selection, cold start mitigation, and adapting DevOps techniques. QFaaS offers a full-stack and unified quantum serverless platform by integrating multiple well-known quantum software development kits (Qiskit, Q#, Cirq, and Braket), quantum simulators, and cloud providers (IBM Quantum and Amazon Braket). This paper proposes the concept of quantum function-as-a-service, system design, operation workflows, implementation of QFaaS, and lessons learned on the benefits and limitations of quantum serverless computing. We also present practical use cases with various quantum applications on today’s quantum computers and simulators to demonstrate our framework capability to facilitate the ongoing quantum software transition.

Archetypal Resonances Between Realms: The Fractal Interplay of Chaos and Order

The intricate balance between chaos and order has fascinated humans for centuries, serving as a recurring theme in culture, psychology, and science. Carl Jung’s insights into archetypes reveal cultural patterns that emerge nearly universally across the globe, independent of history. This paper connects archetypal psychology with contemporary mathematical and quantum concepts. We focus on the profound interconnectedness at the interface between chaos and order, by demonstrating how the Mandelbrot set from contemporary fractal geometry circles round to embody the Oroboros, an ancient symbol of recursive dynamics. Our research bridges micro and macro realms, symbolic meanings, and empirical data, as well as psychological and physical dimensions. By merging age-old symbols with cutting-edge mathematical and quantum ideas, we shed light on the intricate dance of chaos and to underscore the unified nature of existence.

The quantum hypercube as a k-mer graph.

The application of quantum principles in computing has garnered interest since the 1980s. Today, this concept is not only theoretical, but we have the means to design and execute techniques that leverage the quantum principles to perform calculations. The emergence of the quantum walk search technique exemplifies the practical application of quantum concepts and their potential to revolutionize information technologies. It promises to be versatile and may be applied to various problems. For example, the coined quantum walk search allows for identifying a marked item in a combinatorial search space, such as the quantum hypercube. The quantum hypercube organizes the qubits such that the qubit states represent the vertices and the edges represent the transitions to the states differing by one qubit state. It offers a novel framework to represent k-mer graphs in the quantum realm. Thus, the quantum hypercube facilitates the exploitation of parallelism, which is made possible through superposition and entanglement to search for a marked k-mer. However, as found in the analysis of the results, the search is only sometimes successful in hitting the target. Thus, through a meticulous examination of the quantum walk search circuit outcomes, evaluating what input-target combinations are useful, and a visionary exploration of DNA k-mer search, this paper opens the door to innovative possibilities, laying down the groundwork for further research to bridge the gap between theoretical conjecture in quantum computing and a tangible impact in bioinformatics.

Interactive visualisation for teaching a quantum double slit experiment

In teaching quantum physics, visualisation is a useful tool to improve students’ understanding of phenomena from the quantum realm. The double slit experiment has shown itself to be a good simple enough example where all important quantum concepts such as wave-particle duality, superposition, or measurement meet in a nice way. Compiling advantages of existing visualizations, we present a new simple web-based interactive interface visualising the double slit experiment with electrons suitable for high school level. Guidelines for using the visualization in classroom are also provided. Teachers and students would be able to conduct this experiment by themselves and explore behaviour of quantum objects step-by-step, following a path outlined by Richard Feynman in his famous lectures.

Computer models as a means of improving the effectiveness of teaching physics

Computer models and programs are one of the main tools in education, therefore, the development of a plan for their development and use in the field of education is one of the main problems. The use of computer models will help to explore a new topic, a demonstration experiment and phenomena without violating safety regulations. Many experts believe that the computer currently makes it possible to make a qualitative breakthrough in the education system. Models of physical phenomena and experiments actively shape students' knowledge. In teaching a number of sections of the physics course, such as atomic and nuclear physics, quantum mechanics, and elementary particle physics, essential questions about conducting experiments are obvious. These sections relate to important areas of physics that deal with the study of phenomena and processes in the microcosm. Therefore, due to some difficulties in equipping physics classrooms, the computer acts as an assistant. In quantum physics and atomic physics, computer models are considered that help explain the phenomena under study, the course of processes, as well as methods of working with computer programs that simulate laboratory installations in this section, since physical laboratory assistants are an integral part of training. The use of computer models and programs for educational purposes gives students a unique opportunity to plunge into the world of quantum and atomic physics. This study analyzes the effectiveness of such models in the educational process, their impact on students' understanding of the basic concepts of quantum and atomic physics, and also compiles questionnaires based on these problems. The survey covers about 40 physics teachers. The work is based on the analysis of existing pedagogical experiments and research in the field of application of computer models for teaching physics. The focus is on assessing the impact of these models on the quality of knowledge and their ability to make complex concepts accessible and understandable to students. The obtained results can serve as a basis for further improvement of methods of teaching quantum and atomic physics using computer programs. The introduction of computer programs can help the student create an effective learning environment for his work at his own pace and in collaboration with the class. It can be said that the use of models of physical processes in preparing students for effective learning opens up great opportunities for creating high-quality and new forms and methods, the use of computer models of physical phenomena plays an important role. Of particular importance in the development of students' abilities to observe, think, generalize based on observed facts, and predict the course of the observed process.

The Quantum Concept of Consciousness: For or Against?

The study examines a problematic hypothesis of possible approaches to identifying the quantum physical foundations of the functioning of consciousness. The authors proceed from the fact that in modern conditions, not a single science, nor all sciences taken together, gives a final answer to the question of the “mechanism” of the origin of thought. However, this does not mean at all that research in this direction needs to be stopped. The authors express confidence that modern and subsequent research into the “quantum concept of consciousness” will lead to the identification of previously unknown patterns, opening the way to the formation of new principles and approaches. As an example, the corresponding Penrose - Hameroff concept is considered. Quantum mechanics complements the tools of neurobiology and other branches of neuroscience, which together form an interdisciplinary field of knowledge that is dynamically growing and developing. The authors are not apologists for the omnipotence of quantum physics. Quantum correlates of consciousness actually mean that it is not today’s quantum mechanics itself that explains the emergence of mental states, but the fact that in the birth of these states it is essential that in the very process of the formation of neurodynamic impulses in the neurons of the cerebral cortex that generate mental states, there are processes of quantum nature. It should also be recognized that the quantum-molecular level (nanolevel) of processes in the neurons of the brain really exists and it is this that is the source of proto-consciousness. Science strives to move forward, new research programs are emerging within the framework of quantum biology, quantum psychology, quantum information science, which in turn can shed light on the hypothesis of the “quantum concept of consciousness.”

Quantum concepts in Psychology: Exploring the interplay of physics and the human psyche

This paper delves into the innovative intersection of quantum mechanics and psychology, examining the potential of quantum principles to provide fresh insights into human emotions, cognition, and consciousness. Drawing parallels between quantum phenomena such as superposition, entanglement, tunneling, decoherence and their psychological counterparts, we present a quantum-psychological model that reimagines emotional states, cognitive breakthroughs, interpersonal relationships, and the nature of consciousness. The study uses computational models and simulations to explore this interdisciplinary fusion's implications and applications, highlighting its potential benefits and inherent challenges. While quantum concepts offer a rich metaphorical lens to view the intricacies of human experience, it is essential to approach this nascent framework with enthusiasm and skepticism. Rigorous empirical validation is paramount to realize its full potential in research and therapeutic contexts.This exploration stands as a promising thread in the tapestry of intellectual history, suggesting a deeper understanding of the human psyche through the lens of quantum mechanics.

Computational projects with the Landau–Zener problem in the quantum mechanics classroom

The Landau–Zener problem, where a minimum energy separation is passed with constant rate in a two-state quantum-mechanical system, is an excellent model quantum system for a computational project. It requires a low-level computational effort, but has a number of complex numerical and algorithmic issues that can be resolved through dedicated work. It can be used to teach computational concepts, such as accuracy, discretization, and extrapolation, and it reinforces quantum concepts of time-evolution via a time-ordered product and of extrapolation to infinite time via time-dependent perturbation theory. In addition, we discuss the concept of compression algorithms, which are employed in many advanced quantum computing strategies, and easy to illustrate with the Landau–Zener problem.

Applications of Fractional Differential Operator to Subclasses of Uniformly q-Starlike Functions

In this paper, we use the concept of quantum (or q-) calculus and define a q-analogous of a fractional differential operator and discuss some of its applications. We consider this operator to define new subclasses of uniformly q-starlike and q-convex functions associated with a new generalized conic domain, Λβ,q,γ. To begin establishing our key conclusions, we explore several novel lemmas. Furthermore, we employ these lemmas to explore some important features of these two classes, for example, inclusion relations, coefficient bounds, Fekete–Szego problem, and subordination results. We also highlight many known and brand-new specific corollaries of our findings.

Quantum-Inspired Genetic Algorithms for Combinatorial Optimization Problems

Quantum-Inspired Genetic Algorithms (QIGAs) are a trailblazing force in the ever-evolving field of optimization, combining traditional genetic algorithms with quantum concepts to solve challenging combinatorial problems. By contrasting QIGAs with traditional Genetic Algorithms (GAs) in the setting of the Traveling Salesman Problem (TSP), this study explores the potential of QIGAs. The research reveals the transformational potential of quantum-inspired techniques through a thorough investigation of convergence speed, solution quality, and scalability.

Stochastic and corpuscular theory of (polarized) light

Both the corpuscular theory of light and the theory of stochastic processes are well known in the literature. However, they are not systematically used together for description of optical phenomena. There are optical phenomena, such as the well-known three-polarizer experiment or other phenomena related to polarization of light, which have never been quantitatively and qualitatively explained using the concept of quantum of light (photon). The situation changed in 2022 when stochastic memoryless and independent (IM) process formulated within the framework of the theory of stochastic processes was introduced. It is suitable for determination of probability (density) functions characterizing interaction (transmission or reflection) of individual photons with optical elements on the basis of experimental data. The process has memoryless (Markov) property, and it is assumed that the interactions of individual photons with an optical system are independent. Formulae needed for analysis of data in the context of polarization of light are derived. An example analysis of the three-polarizer experiment is performed and numerical result of the probability (density) functions are determined. These original results were missing in the literature. The results imply that the possibilities of the corpuscular theory of light to describe optical phenomena can be significantly extended with the help of stochastic IM process and the theory of stochastic processes in general.

Probing DDM and ML quantum concepts in shape phase transitions of γ-unstable nuclei

In a recent paper (S. Ait El Korchi et al. (2020) [32]), we explored, inside the context of Critical Point Symmetries (CPSs) X(3) and Z(4), a correlation between two exceedingly known quantum concepts, the Minimal Length (ML) and the Deformation-Dependent Mass (DDM), that are commonly applied in various areas of physics. Such a correlation has been strongly identified in transition nuclei by calculating some physical observables of that quantum system, like as energy spectra, moments of inertia and transition probabilities. In this paper we extend that study to E(5) dynamical symmetry corresponding to the shape phase transition U(5)↔O(6). The experimental realization of the models was found to occur in some nuclei, using the existing phenomenological potentials: Infinite Square Well, Davidson and Kratzer, whose models fits provide the best agreement. Importantly the calculations performed in this work using these potentials, corroborate the fact that the revealed correlation between both quantum concepts is not destructively affected by the presence of other model's parameters and hence its existence is independent of the form or type of the used potential. Undoubtedly, the present work will open the way for more investigations of this correlation in the limits of other critical points symmetries in nuclear shape phase transitions which play today a major role in nuclear structure research from theoretical as well as experimental point of view.

Exploring the relationship between students’ conceptual understanding and model thinking in quantum optics

Learning quantum physics is essential for understanding the physical world. However, learning about quantum phenomena and principles poses a challenge as many of the phenomena that are observed at the quantum level cannot be directly observed or intuitively understood in terms of classical physics or thinking. Models play an important role in learning quantum physics by providing conceptual frameworks and visual representations that allow reasoning about and predicting the behavior of quantum systems. Therefore, understanding models is an essential part of learning quantum physics. In this article, we report the results of an exploratory survey study (N = 116) investigating the relationship between secondary school students’ conceptual understanding and model thinking in quantum optics with a particular focus on photons. The findings suggest a strong positive correlation between students’ functional understanding of the photon model and their conceptual understanding of quantum optics. This study contributes to our understanding of how students learn and make sense of quantum concepts through the use of models and may inform the development of instructional strategies for quantum physics education and outreach.

Is everything quantum ‘spooky and weird’? An exploration of popular communication about quantum science and technology in TEDx talks

Previous studies have identified four potential issues related to the popularisation of quantum science and technology. These include framing quantum science and technology as spooky and enigmatic, a lack of explaining underlying quantum concepts of quantum 2.0 technology, framing quantum technology narrowly in terms of public good and having a strong focus on quantum computing. Before assessing the effect of these potential issues on public perceptions, it is important to first determine whether these issues are actually present in popular communication. To this end, we conducted a content analysis in which we investigated how quantum science and technology are framed in a corpus of 501 TEDx talks. We also examined to what extent quantum experts, such as quantum scientists and leaders at organisations in quantum science and technology, communicate about quantum science and technology differently from non-experts, such as scientists from other disciplines and artists. Results showed that: (1) about a quarter of the talks framed quantum science and technology as spooky/enigmatic; (2) about half of the talks explained at least one underlying quantum concept (superposition, entanglement or contextuality) of quantum 2.0 technology; (3) quantum technology is narrowly framed in terms of public good as we found six times more talks mentioning benefits than risks; and (4) the main focus is on quantum computing at the expense of other quantum technologies. In addition, experts and non-experts differ on three out of four issues (only the fourth issue is similar for both). Our findings thus show that these potential issues related to the popularisation of quantum science and technology are present but not predominant in TEDx talks. Further research should explore their effect on public perceptions of quantum science and technology.

Quantum Computing Approaches for Vector Quantization-Current Perspectives and Developments.

In the field of machine learning, vector quantization is a category of low-complexity approaches that are nonetheless powerful for data representation and clustering or classification tasks. Vector quantization is based on the idea of representing a data or a class distribution using a small set of prototypes, and hence, it belongs to interpretable models in machine learning. Further, the low complexity of vector quantizers makes them interesting for the application of quantum concepts for their implementation. This is especially true for current and upcoming generations of quantum devices, which only allow the execution of simple and restricted algorithms. Motivated by different adaptation and optimization paradigms for vector quantizers, we provide an overview of respective existing quantum algorithms and routines to realize vector quantization concepts, maybe only partially, on quantum devices. Thus, the reader can infer the current state-of-the-art when considering quantum computing approaches for vector quantization.

Organic Synthetic Photonic Systems with Reconfigurable Parity-Time Symmetry Breaking for Tunable Single-Mode Microlasers.

Synthetic photonic materials exploiting the quantum concept of parity-time (PT) symmetry lead to an emerging photonic paradigm-non-Hermitian photonics, which is revolutionizing the photonic sciences. The non-Hermitian photonics dealing with the interplay between gain and loss in PT synthetic photonic material systems offers a versatile platform for advancing microlaser technology. However, current PT-symmetric microcavity laser systems only manipulate imaginary parts of the refractive indices, suffering from limited laser spectral bandwidth. Here, an organic composite material system is proposed to synthesize reconfigurable PT-symmetric microcavities with controllable complex refractive indices for realizing tunable single-mode laser outputs. A grayscale electron-beam direct-writing technique is elaborately designed to process laser dye-doped polymer films in one single step into microdisk cavities with periodic gain and loss distribution, which enables thresholdless PT-symmetry breaking and single-mode laser operation. Furthermore, organic photoisomerizable compounds are introduced to reconfigure the PT-symmetric systems in real-time by tailoring the real refractive index of the polymer microresonators, allowing for a dynamically and continuously tunable single-mode laser output. This work fundamentally enhances the PT-symmetric photonic systems for innovative design of synthetic photonic materials and architectures.