Principles Of Quantum Mechanics Research Articles

Information entropies with Varshni-Hellmann potential in higher dimensions

This work investigates the behavior of Shannon entropy and Fisher information for the Varshni-Hellmann potential (VHP) in one and three dimensions using the Nikiforov-Uvarov method. We employ the Greene-Aldrich approximation scheme to obtain the energy eigenvalues and normalized wavefunctions, which are then used to calculate these information-theoretic quantities. Our analysis revealed remarkably similar high-order features in both position and momentum spaces. Notably, our calculations showed enhanced accuracy in predicting particle localization within position space. Furthermore, the combined position and momentum entropies obeyed the lower and upper bounds established by the Berkner-Bialynicki-Birula-Mycieslki inequality. Additionally, for three-dimensional systems, the Stam-Cramer-Rao inequalities were fulfilled for different eigenstates with respect to the calculated Fisher information. It is observed that as the position Fisher entropy decreases, indicating a more precise measurement of position, the momentum Fisher entropy must increase. This implies that the Fisher information regarding momentum decreases, resulting in a decrease in the precision of momentum measurement. This demonstrates how position and momentum uncertainties complement each other in quantum mechanics. Exploring the balance between position and momentum Fisher entropy reveals a fundamental aspect of the uncertainty principle in quantum mechanics, highlighting the restrictions on measuring certain pairs of conjugate variables simultaneously with high precision.

Chip-Based Electronic System for Quantum Key Distribution

Quantum Key Distribution (QKD) has garnered significant attention due to its unconditional security based on the fundamental principles of quantum mechanics. While QKD has been demonstrated by various groups and commercial QKD products are available, the development of a fully chip-based QKD system, aimed at reducing costs, size, and power consumption, remains a significant technological challenge. Most researchers focus on the optical aspects, leaving the integration of the electronic components largely unexplored. In this paper, we present the design of a fully integrated electrical control chip for QKD applications. The chip, fabricated using 28 nm CMOS technology, comprises five main modules: an ARM processor for digital signal processing, delay cells for timing synchronization, ADC for sampling analog signals from monitors, OPAMP for signal amplification, and DAC for generating the required voltage for phase or intensity modulators. According to the simulations, the minimum delay is 11ps, the open-loop gain of the operational amplifier is 86.2 dB, the sampling rate of the ADC reaches 50 MHz, and the DAC achieves a high rate of 100 MHz. To the best of our knowledge, this marks the first design and evaluation of a fully integrated driver chip for QKD, holding the potential to significantly enhance QKD system performance. Thus, we believe our work could inspire future investigations toward the development of more efficient and reliable QKD systems.

Measuring the Density Matrix of Quantum-Modeled Cognitive States

Inspired by the principles of quantum mechanics, we constructed a model of students’ misconceptions about heat and temperature, conceptualized as a quantum system represented by a density matrix. Within this framework, the presence or absence of misconceptions is delineated as pure states, while the probability of mixed states is also considered, providing valuable insights into students’ cognition based on the mental models they employ when holding misconceptions. Using the analysis model previously employed by Lei Bao and Edward Redish, we represented these results in a density matrix. In our research, we utilized the Zeo and Zadnik Thermal Concept Evaluation among 282 students from a private university in Northeast Mexico. Our objective was to extract information from the analysis of multiple-choice questions designed to explore preconceptions, offering valuable educational insights beyond the typical Correct–Incorrect binary analysis of classical systems. Our findings reveal a probability of 0.72 for the appearance of misconceptions, 0.28 for their absence, and 0.43 for mixed states, while no significant disparities were observed based on gender or scholarship status, a notable difference was observed among programs (p < 0.05). These results are consistent with the previous literature, confirming a prevalence of misconceptions within the student population.

Quantum Cryptography: Advancements, Challenges, and Applications in Modern Communication

This research paper explores the fascinating field of Quantum Cryptography, a cutting-edge technology that leverages principles of quantum mechanics to secure information transfer. The objective of this study is to delve into the underlying principles of Quantum Cryptography, specifically Quantum Key Distribution (QKD), and discuss its potential applications and challenges. The methodology involves a comprehensive review of existing literature and recent advancements in the field. The key findings reveal that Quantum Cryptography presents a promising solution for secure communication, offering robust defence against potential eavesdroppers. However, practical implementation faces several challenges, including technological limitations and the need for standardization. The implications of this study underscore the transformative potential of Quantum Cryptography in shaping the future of secure communication and highlight the need for further research and development in overcoming existing challenges.

Testing Multi-Subroutine Quantum Programs: From Unit Testing to Integration Testing

Quantum computing has emerged as a promising field with the potential to revolutionize various domains by harnessing the principles of quantum mechanics. As quantum hardware and algorithms continue to advance, developing high-quality quantum software has become crucial. However, testing quantum programs poses unique challenges due to the distinctive characteristics of quantum systems and the complexity of multi-subroutine programs. This paper addresses the specific testing requirements of multi-subroutine quantum programs. We begin by investigating critical properties by surveying existing quantum libraries and providing insights into the challenges of testing these programs. Building upon this understanding, we focus on testing criteria and techniques based on the whole testing process perspective, spanning from unit testing to integration testing. We delve into various aspects, including IO analysis, quantum relation checking, structural testing, behavior testing, integration of subroutine pairs, and test case generation. We also introduce novel testing principles and criteria to guide the testing process. We conduct comprehensive testing on typical quantum subroutines, including diverse mutants and randomized inputs, to evaluate our proposed approach. The analysis of failures provides valuable insights into the effectiveness of our testing methodology. Additionally, we present case studies on representative multi-subroutine quantum programs, demonstrating the practical application and effectiveness of our proposed testing principles and criteria.

Equivalence principle for quantum mechanics in the Heisenberg picture

We present an exact quantum observable analog of the weak equivalence principle for a ‘relativistic’ quantum particle. The quantum geodesic equations are obtained from Heisenberg equations of motion as an exact analog of a fully covariant classical Hamiltonian evolution picture, with the proper identification of the canonical momentum variables as p µ , rather than p µ . We discuss the meaning of the equations in relation to projective measurements as well as equations with solution curves as ones in the noncommutative geometric picture of spacetime, and a plausible approach to quantum gravity as a theory about quantum observables as physical quantities including the notion of quantum coordinate transformation.

Brief Introduction to Quantum Computing for Undergraduate Students: Lecture One

This article provides an introductory overview of quantum computing for college students through intuitive examples. We explore key concepts, starting with the basic principles of quantum mechanics. The discussion covers essential elements such as Qubits, superposition, entanglement, and introduces quantum gates. The article concludes by examining the first quantum algorithm: the solution to Deutsch's Problem.

Implementing an environment for hybrid software evaluation

Quantum computing is a revolutionary paradigm in computer science based on the principles of quantum mechanics. It has the potential to solve problems that are currently unsolvable for classical computing. Applications of quantum computing already span a variety of sectors.Ongoing enhancements to the integrated programming and development environment simplify the creation and optimization of quantum algorithms. Ultimately, the focus on supporting tools represents the starting point towards achieving quantum computing maturity, facilitating its transition from an experimental domain to a practical industry.As quantum software gains ground and relevance in various domains, it is essential to address the evaluation of hybrid systems that combine classical and quantum elements to ensure diverse quality characteristics. However, in the realm of quantum software, models, metrics, and tools are still to be established.The primary contribution of this paper is to present the first technological environment for measuring and evaluating the analyzability of hybrid software.Real-world examples of hybrid software are provided to showcase the functionality of the different tools in the environment, yielding readable and representative results for the evaluator.

Derivation of Dirac equation from the stochastic optimal control principles of quantum mechanics.

In this paper, we present a stochastic approach to relativistic quantum mechanics. We formulate the three fundamental principles of this theory and derive the Dirac equations based on them. This approach enables us to bring more insight into the nature of Dirac's spinors. Furthermore, we provide a physical interpretation of the stochastic optimal control theory of quantum mechanics.

Novel quantum solutions to privacy-preserving point-line relation determination

Secure multiparty computational geometry is an essential field of secure multiparty computation. It involves solving geometric problems without disclosing any private geometric information from each participating party. Privacy-preserving point-line relation determination, a pivotal branch of secure multiparty computational geometry, holds significant potential for applications in various domains, including business, engineering, and military. In this paper, leveraging the assistance of a third party, we introduce a quantum solution to privacy-preserving point-line relation determination. This approach incorporates quantum key distribution and one-time pad encryption. Under the condition that the third party does not conspire with any participant, our protocol ensures heightened security and enhanced privacy protection compared to classical methods. This superiority is attributed to the underlying principles of quantum mechanics and the utilization of one-time pad encryption. Furthermore, we extend our protocol to involve multiple third parties, employing the technology of quantum secret sharing. In scenarios where these third parties refrain from colluding with any single participant, no information is divulged to the other participant. Consequently, the protocol becomes more rational and secure when multiple third parties are involved.

The quantum mechanics of skincare: A context for the biochemistry curriculum.

Designing a relevant and engaging curriculum for biochemistry undergraduates can be challenging for topics which are at the periphery of the subject. We have used the framework of context-based learning as a means of assessing understanding of quantum theory in a group of students in their junior year. Our context, the role of retinol in skincare, provides a basis for the simple application of quantum mechanical principles to a biological context in an adaptation of the polyene in a box concept. As part of the learner journey, they gain experience of practical computational chemistry, which provided an in silico alternative to traditional laboratory work during the SARS-CoV-19 pandemic. Student feedback was overwhelmingly positive, and this approach is now firmly embedded in the undergraduate curriculum.

Explaining Grover’s algorithm with a colony of ants: a pedagogical model for making quantum technology comprehensible

The rapid growth of quantum technologies requires an increasing number of physicists, computer scientists, and engineers who can work on these technologies. For educating these professionals, quantum mechanics should stop being perceived as incomprehensible. In this paper we contribute to this change by presenting a pedagogical model for explaining Grover’s search algorithm, a prominent quantum algorithm. This model visualizes the three main steps of Grover’s algorithm and, in addition to explaining the algorithm itself, introduces three key principles of quantum mechanics: superposition, interference, and state collapse at measurement. The pedagogical model, visualized by a video, is called the ant colony maze model. It represents the search problems as finding the exit of a maze, and visualizes Grover’s search algorithm as a strategy by which a colony of ants finds that exit.

Continuous-variable quantum key distribution system: Past, present, and future

Quantum key distribution provides secure keys with information-theoretic security ensured by the principle of quantum mechanics. The continuous-variable version of quantum key distribution using coherent states offers the advantages of its compatibility with telecom industry, e.g., using commercial laser and homodyne detector, is now going through a booming period. In this review article, we describe the principle of continuous-variable quantum key distribution system; focus on protocols based on coherent states, whose systems are gradually moving from proof-of-principle lab demonstrations to in-field implementations and technological prototypes. We start by reviewing the theoretical protocols and the current security status of these protocols. Then, we discuss the system structure, the key module, and the mainstream system implementations. The advanced progresses for future applications are discussed, including the digital techniques, system on chip, and point-to-multipoint system. Finally, we discuss the practical security of the system and conclude with promising perspectives in this research field.

Summation formulas generated by Hilbert space eigenproblem

We demonstrate that certain classes of Schlömilch-like infinite series and series that include generalized hypergeometric functions can be calculated in closed form starting from a simple quantum model of a particle trapped inside an infinite potential well and using principles of quantum mechanics. We provide a general framework based on the Hilbert space eigenproblem that can be applied to different exactly solvable quantum models. Obtaining series from normalization conditions in well-defined quantum problems secures their convergence.

A Simulation of Hydrazine Molecule’s Potential Energy Surface using Variational Quantum Eigensolver Algorithm

Quantum computing is a technology that utilizes the principles of quantum mechanics to perform complex computational processes. In this work, we use Qiskit Module from IBM to do quantum computational calculation using Variational Quantum Eigensolver (VQE) algorithm. VQE is a hybrid quantum-classical method that combines a quantum computer to measure energies and a classical computer to process the measurement results and update the parameters of the quantum computer. The purpose of VQE is to find the ground state energy of a chemical system. In the previous study, many of the VQE calculations have been done on simple molecules. So, in this study, we would like to use Hydrazine molecule as our object of VQE calculation. Furthermore, these results will be compared with the results from the classical calculation (MP2, CCSD(T), QCISD(T), and CASSCF) methods for testing the effectiveness of VQE using Unitary Coupled-Cluster Single and Double excitations (UCCSD) Ansatz. The quantum algorithm based on the UCCSD Ansatz led to a simplification of the algorithm by reducing the circuit depth. Then, the possibility to use active space approximation, can be used to reduce the quantum gates while trying to keep a good level of accuracy. In this study, we chose (2,2) and (4,4) active spaces. Based on the results, as we increase the size of the active space during the evaluation of the single-point energy, the estimated ground states obtained from the VQE algorithm yield nearly identical values. Conversely, in CASSCF calculations, expanding the active space introduces more energy corrections, thus making it more sensitive. Additionally, when examining potential energy surfaces, VQE demonstrates results that gradually align with CCSD(T) and QCISD(T) methods.

Quantum machine learning for image classification

Image classification, a pivotal task in multiple industries, faces computational challenges due to the burgeoning volume of visual data. This research addresses these challenges by introducing two quantum machine learning models that leverage the principles of quantum mechanics for effective computations. Our first model, a hybrid quantum neural network with parallel quantum circuits, enables the execution of computations even in the noisy intermediate-scale quantum era, where circuits with a large number of qubits are currently infeasible. This model demonstrated a record-breaking classification accuracy of 99.21% on the full MNIST dataset, surpassing the performance of known quantum–classical models, while having eight times fewer parameters than its classical counterpart. Also, the results of testing this hybrid model on a Medical MNIST (classification accuracy over 99%), and on CIFAR-10 (classification accuracy over 82%), can serve as evidence of the generalizability of the model and highlights the efficiency of quantum layers in distinguishing common features of input data. Our second model introduces a hybrid quantum neural network with a Quanvolutional layer, reducing image resolution via a convolution process. The model matches the performance of its classical counterpart, having four times fewer trainable parameters, and outperforms a classical model with equal weight parameters. These models represent advancements in quantum machine learning research and illuminate the path towards more accurate image classification systems.

Quantum-Assisted Activation for Supervised Learning in Healthcare-Based Intrusion Detection Systems

Intrusion detection systems (IDS) are amongst the most important automated defense mechanisms in modern industry. It is guarding against many attack vectors, especially in healthcare, where sensitive information (patient’s medical history, prescriptions, electronic health records, medical bills/debts, and many other sensitive data points) is open to compromise from adversaries. In the big data era, classical machine learning has been applied to train IDS. However, classical IDS tend to be complex: either using several hidden layers susceptible to over-fitting on training data or using overly complex architectures such as convolutional neural networks (CNNs), long-short term memory systems (LSTMs), and recurrent neural networks (RNNs). This paper explored the combination of principles of quantum mechanics and neural networks to train IDS. A hybrid classical-quantum neural architecture is proposed with a quantum-assisted activation function that successfully captures patterns in the dataset while having less architectural memory footprint than classical solutions. The experimental results are demonstrated on the popular KDD99 dataset while comparing our solution to other classical models.

Exploring and reviewing the potential of quantum computing in enhancing cybersecurity encryption methods

As the landscape of cybersecurity continually evolves, traditional encryption methods face unprecedented challenges from the impending era of quantum computing. This paper undertakes a comprehensive exploration of the potential transformative impact that quantum computing could have on enhancing cybersecurity encryption methods. Commencing with an overview of quantum computing fundamentals, including the principles of quantum mechanics and key quantum properties, the paper delves into the disruptive power of Shor's algorithm. This algorithm, capable of exponentially faster factorization than classical counterparts, poses a significant threat to prevalent cryptographic techniques such as RSA and ECC. In response to the vulnerabilities exposed by quantum algorithms, the paper investigates the field of post-quantum cryptography, examining cryptographic algorithms designed to resist quantum attacks. Additionally, the study scrutinizes Quantum Key Distribution (QKD) as a potential solution for secure communication in a quantum environment, analyzing its strengths and limitations. The paper provides an updated survey of the current state of quantum computing, highlighting achievements, milestones, and a comparative analysis of existing quantum computing platforms. Subsequently, it assesses the potential impact of quantum computing on cybersecurity, addressing both its ability to fortify encryption and potential risks and vulnerabilities. Striking a balance between benefits and challenges, the research offers insights into the coexistence of quantum and classical cryptographic methods. Looking toward the future, the paper explores ongoing research and development in quantum computing, identifying challenges and ethical considerations. In conclusion, it synthesizes key findings, emphasizing the implications for the future of cybersecurity and advocating for continued research to ensure the development of resilient encryption methods in the quantum era.

Quantum Computing in The Cloud - A Systematic Literature Review

Quantum computing was proposed to simulate processes that surpass the capabilities of its counterpart, classical computing. Utilizing the principles of quantum mechanics, it improves the computing power of quantum computing. Top developers namely IBM, Rigetti, D-Wave, Qutech and Google have invested greatly in the technology. Nowadays, users can access the quantum computing system publicly over the network in a cloud environment, this system architecture is known as cloud-based quantum computing. However, different developers deliver different architecture and functionality of the system on their platforms. This has indirectly spawned a question of which cloud-based quantum computing platform is a better option based on certain specific requirements by an individual or group. The main objective of this study is to provide a proposed framework using the existing cloud-based service of quantum computing based on previous studies for users with their specific demands.

A novel quantum key distribution resistant against large‐pulse attacks

AbstractQuantum key distribution (QKD) offers information‐theoretic security by leveraging the principles of quantum mechanics. This means the security is independent of all future advances in algorithm or computational power. However, due to the non‐availability of single‐photon sources, most traditional QKD protocols are vulnerable to various attacks, such as photon number‐splitting (PNS) attacks. Also, the imperfections in the measuring devices open a loophole for side channels that an eavesdropper may exploit to launch attacks such as large‐pulse attacks. As a result, this compromises the security of transmitted information. To address these challenges, the authors present a QKD protocol that is secure against both large‐pulse attacks and PNS attacks at zero‐error, in which the eavesdropper does not introduce any error, but still, the legitimate users of the system cannot distil a secure key. A notable feature of the proposed protocol is that it promotes greater robustness against both attacks than the Bennett‐Brassard 1984 (BB84) protocol or the Scarani‐Acin‐Ribordy‐Gisin 2004 (SARG04) protocol.