Integrable Quantum Research Articles

Quantum Algorithms for Image Processing: Enhancing Computational Efficiency and Accuracy in High-Dimensional Visual Data Analysis

Quantum algorithms have emerged as a transformative approach to address the computational challenges of high-dimensional image processing tasks. This research investigates the integration of quantum computing principles, such as Quantum Fourier Transform (QFT) and Quantum Principal Component Analysis (QPCA), to optimize processes like edge detection, noise reduction, and image segmentation. These quantum-enhanced techniques promise significant improvements in computational efficiency and accuracy compared to classical methods, especially when handling complex visual data in real-time applications like medical imaging, satellite imagery, and autonomous systems. Additionally, the study explores hybrid quantum-classical architectures to bridge current limitations in noisy intermediate-scale quantum (NISQ) devices, ensuring resource optimization and scalability. The potential of quantum algorithms to provide faster, more precise solutions is evaluated alongside challenges like error mitigation and algorithmic stability. This research highlights the future role of quantum computing in revolutionizing image processing, paving the way for breakthroughs in computer vision and artificial intelligence.

Controlling Energy Storage Crossing Quantum Phase Transitions in an Integrable Spin Quantum Battery.

We investigate the performance of a one-dimensional dimerized XY chain as a spin quantum battery. Such integrable model shows a rich quantum phase diagram that emerges through a mapping of the spins onto auxiliary fermionic degrees of freedom. We consider a charging protocol relying on the double quench of an internal parameter, namely the strength of the dimerization, and address the energy stored in the systems. We observe three distinct regimes, depending on the timescale characterizing the duration of the charging: a short-time regime related to the dynamics of the single dimers, a long-time regime related to the recurrence time of the system at finite size, and a thermodynamic limit time regime. In the latter, the energy stored is almost unaffected by the charging time and the precise values of the charging parameters, provided the quench crosses a quantum phase transition. Finally, we analytically prove that the three-timescale behavior and the strong dependence of the energy stored on the quantum phase diagram also hold in the quantum Ising chain in a transverse field. Our results can play a relevant role in the design of stable solid-state quantum batteries.

Topological 4D gravity and gravitational defects

Using the Chern-Simons formulation of AdS3 gravity as well as the Costello-Witten-Yamazaki (CWY) theory for quantum integrability, we construct a novel topological 4D gravity given by equation (5.1) with observables based on gravitational gauge field holonomies. The field action S4Dgrav of this gravity has a gauge symmetry SL(2,C) and reads also as the difference S4DCWYL−S4DCWYR with 4D Chern-Simons field actions S4DCWYL/R given by left/right CWY theory equation (3.9). We also use this 4D gravity derivation to build observables describing gravitational topological defects and their interactions. We conclude our study with few comments regarding quantum integrability and the extension of AdS3/CFT2 correspondence with regard to the obtained topological 4D gravity.

Simpson Type Estimations for Convex Functions via Quantum Calculus

We first establish a new identity including quantum integrals and quantum numbers via q -differentiable functions. After that, with the help of this equality, a Simpson-type inequality for functions whose quantum derivatives in modulus are convex is derived, and some new inequalities for powers of quantum derivatives in absolute value are provided. It is also discussed how results come out in the case when q approaches 1. Mathematics Subject Classification: 26D15, 26D10, 26A51, 34A08.

Exact results of the one-dimensional repulsive Hubbard model

We present analytical results of the fundamental properties of the one-dimensional (1D) Hubbard model with a repulsive interaction. The new model results with arbitrary external fields include: (I) using the exact solutions of the Bethe ansatz equations of the Hubbard model, we first rigorously calculate the gapless spin and charge excitations, exhibiting exotic features of fractionalized spinons and holons. We then investigate the gapped excitations in terms of the spin string and thek-Λstring bound states at arbitrary driving fields, showing subtle differences in spin magnons and chargeη-pair excitations. (II) For a high-density and high spin magnetization region, i.e. near the quadruple critical point, we further analytically obtain the thermodynamic properties, dimensionless ratios and scaling functions near quantum phase transitions. (III) Importantly, we give the general scaling functions at quantum criticality for arbitrary filling and interaction strength. These can directly apply to other integrable models. (IV) Based on the fractional excitations and the scaling laws, the spin-incoherent Luttinger liquid (SILL) with only the charge propagation mode is elucidated by the asymptotic of the two-point correlation functions with the help of conformal field theory. We also, for the first time, obtain the analytical results of the thermodynamics for the SILL. (V) Finally, to capture deeper insights into the Mott insulator and interaction-driven criticality, we further study the double occupancy and propose its associated contact and contact susceptibilities, through which an adiabatic cooling scheme based upon quantum criticality is proposed. In this scenario, we build up general relations among arbitrary external- and internal-potential-driven quantum phase transitions, providing a comprehensive understanding of quantum criticality. Our methods offer rich perspectives of quantum integrability and offer promising guidance for future experiments with interacting electrons and ultracold atoms, both with and without a lattice.

Quantum Computing and Cloud Technologies: The Next Frontier in Computing Power

Abstract: This article explores the convergence of quantum computing and cloud technologies, representing a pivotal advancement in computational power with far-reaching implications across various industries and scientific domains. It examines the current state of quantum computing, elucidating its fundamental principles and recent hardware advancements, while comparing its capabilities to classical computing systems. The integration of quantum computing with cloud platforms is analyzed, highlighting the emergence of cloud-based quantum services and their advantages in democratizing access to this cutting-edge technology. The article delves into potential applications of quantum cloud computing, including cryptography, material science, artificial intelligence, and financial modeling, showcasing its transformative potential. Critical challenges facing quantum cloud computing are addressed, such as error correction, scalability issues, and the development of quantumsafe encryption methods. Looking ahead, the article discusses prospects and research directions, including anticipated breakthroughs in quantum hardware, emerging quantum cloud architectures, and the potential impact on various industries. By synthesizing current research and industry developments, this comprehensive overview provides insights into the revolutionary potential of quantum cloud computing and its role in shaping the future of computational capabilities.

On Bethe equations of 2d conformal field theory

We study the higher spin algebras of two-dimensional conformal field theory from the perspective of quantum integrability. Starting from Maulik-Okounkov instanton R-matrix and applying the procedure of algebraic Bethe ansatz, we obtain infinite commuting families of Hamiltonians of quantum ILW hierarchy parametrized by the shape of the auxiliary torus. We calculate explicitly the first five of these Hamiltonians. Then, we numerically verify that their joint spectrum can be parametriezed by solutions of Litvinov’s Bethe ansatz equations and we conjecture a general formula for the joint spectrum of all ILW Hamiltonians, based on results of Feigin, Jimbo, Miwa and Mukhin.There are two interesting degeneration limits, the infinitely thick and the infinitely thin auxiliary torus. In one of these limits, the ILW hierarchy degenerates to Yangian or Benjamin-Ono hiearchy and the Bethe equations can be easily solved. The other limit is singular but we can nevertheless extract local Hamiltonians corresponding to quantum KdV or KP hierarchy. Litvinov’s Bethe equations in this local limit provide an alternative to Bethe ansatz equations of Bazhanov, Lukyanov and Zamolodchikov, but are more transparent, work at any rank and are manifestly symmetric under triality symmetry of W\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{W} $$\\end{document}1+∞. Finally, we illustrate analytic properties of the solutions of Bethe equations in minimal models, in particular for Lee-Yang CFT. The analytic structure of Bethe roots is very rich as it captures the representation theory of W\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{W} $$\\end{document}N minimal models.

Statistics of Matrix Elements of Local Operators in Integrable Models

We study the statistics of matrix elements of local operators in the basis of energy eigenstates in a paradigmatic, integrable, many-particle quantum theory, the Lieb-Liniger model of bosons with repulsive delta-function interactions. Using methods of quantum integrability, we determine the scaling of matrix elements with system size. As a consequence of the extensive number of conservation laws, the structure of matrix elements is fundamentally different from, and much more intricate than, the predictions of the eigenstate thermalization hypothesis for generic models. We uncover an interesting connection between this structure for local operators in interacting integrable models and the one for local operators that are not local with respect to the elementary excitations in free theories. We find that typical off-diagonal matrix elements ⟨μ|O|λ⟩ in the same macrostate scale as exp(−cOLln(L)−LMμ,λO), where the probability distribution function for Mμ,λO is well described by Fréchet distributions and cO depends only on macrostate information. In contrast, typical off-diagonal matrix elements between two different macrostates scale as exp(−dOL2), where dO depends only on macrostate information. Diagonal matrix elements depend only on macrostate information up to finite-size corrections. Published by the American Physical Society 2024

Quantum Machine Learning: Leveraging Quantum Computing for Enhanced Learning Algorithms

The paper "Quantum Machine Learning: Leveraging Quantum Computing for Enhanced Learning Algorithms" explores the integration of quantum computing principles into classical machine learning techniques, aiming to address limitations such as scalability and computational inefficiency. It presents the foundational concepts of quantum computing, including superposition and entanglement, and their application in accelerating machine learning processes. The study emphasizes the potential for quantum algorithms to significantly improve the performance of machine learning tasks by processing large datasets more efficiently and exploring larger hypothesis spaces. Key quantum machine learning algorithms discussed include Quantum Support Vector Machines (QSVM), Quantum Principal Component Analysis (QPCA), and Quantum Neural Networks (QNN), each of which leverages quantum mechanics to overcome the computational barriers faced by classical algorithms. The Quantum Approximate Optimization Algorithm (QAOA) is also highlighted for its ability to optimize machine learning models more effectively. While the theoretical benefits of Quantum Machine Learning (QML) are promising, the practical application of these techniques is currently limited by the constraints of existing quantum hardware. This research contributes to the emerging field of QML by examining its potential advantages and future implications in addressing complex data processing challenges.

Quantum computing integration with multi-cloud architectures: enhancing computational efficiency and security in advanced cloud environments

The objective of this research is to explore the integration of quantum computing with multi-cloud architectures, aiming to enhance computational efficiency and security in advanced cloud environments. The study seeks to identify the potential benefits and challenges of incorporating quantum computing capabilities within a multi-cloud framework and to evaluate the impact on performance and security metrics. The research employs a hybrid methodological approach, combining both theoretical analysis and practical implementation. Initially, a detailed literature review is conducted to understand the current state of quantum computing and multi-cloud architectures. This is followed by the design and development of an integration framework that leverages quantum computing technologies in a multi-cloud environment. Key steps include developing a multi-cloud architecture that integrates quantum computing resources alongside classical computing resources, deploying quantum algorithms and protocols within the multi-cloud setup, implementing advanced security measures to protect data and computational processes, using a set of predefined metrics to evaluate computational efficiency and security, and employing statistical tools and techniques to analyze the collected data and draw meaningful insights. The integration of quantum computing with multi-cloud architectures resulted in significant improvements in computational efficiency, particularly in tasks that are traditionally resource-intensive. Key findings include enhanced computational speed, where quantum algorithms demonstrated superior performance in solving complex problems compared to classical algorithms, optimized resource utilization through dynamic allocation of quantum and classical resources leading to cost efficiency, improved security with quantum-enhanced protocols providing robust protection against cyber threats, and high scalability of the integrated architecture to accommodate increasing computational demands without compromising performance. The research concludes that integrating quantum computing with multi-cloud architectures offers substantial benefits in terms of computational efficiency and security. The findings indicate that such integration can revolutionize cloud computing, providing a powerful platform for handling complex computations and enhancing data security. However, the study also highlights several challenges, including the need for specialized hardware, the complexity of integration, and the necessity for ongoing research to fully harness the potential of quantum computing in cloud environments. Future research should focus on addressing these challenges and exploring further applications of quantum computing in various cloud-based scenarios.

Revolutionizing Healthcare: The Emerging Role of Quantum Computing in Enhancing Medical Technology and Treatment.

The healthcare sector faces complex challenges that call for innovative solutions to improve diagnostic accuracy, treatment efficacy, and data management. Quantum computing, with its unique capabilities, holds the potential to revolutionize various aspects of healthcare. This narrative review critically examines the existing literature on the application of quantum computing in healthcare, focusing on its utility in enhancing diagnostics, data processing, and treatment planning. Quantum computing's ability to handle large, complex datasets more efficiently than classical computers can significantly impact domains such as genomics, medical imaging, and personalized medicine. Quantum algorithms can accelerate the identification of genetic markers associated with diseases, facilitate the analysis of medical images, and optimize treatment plans based on individual genetic profiles. Moreover, quantum cryptography offers a robust security solution for safeguarding sensitive patient data, a critical need as healthcare increasingly relies on digital platforms. Despite the promising outlook, the integration of quantum computing into healthcare faces technical, ethical, and regulatory challenges. The delicate nature of quantum hardware, the need for error correction, and the scalability of quantum systems pose barriers to widespread adoption. Additionally, concerns around patient privacy and data security, as well as the need for updated regulatory frameworks, must be addressed. Ongoing research and collaborative efforts involving researchers, healthcare providers, and technology developers are crucial to overcoming these hurdles and realizing the full potential of quantum computing in transforming healthcare. As quantum computing continues to evolve, its impact on the future of healthcare could be profound, leading to earlier disease detection, more personalized treatments, and improved patient outcomes.For instance, quantum computing has already been applied to enhance drug discovery processes, with companies like D-Wave Systems (Burnaby, Canada) demonstrating faster molecular simulations for pharmaceutical research and IBM's (Armonk, USA) quantum systems being used to model chemical reactions for new drug development.

Signatures of quantum integrability and exactly solvable dynamics in an infinite-range many-body Floquet spin system

Signatures of quantum integrability and exactly solvable dynamics in an infinite-range many-body Floquet spin system

Investigation of the complex dynamical structure of bifurcation and dark soliton solutions to fractional generalized double [formula omitted]-Gordon equation

In the current research work, the classical wave equation is combined with a nonlinear sinh source term in the sinh-Gordon equation. It has been used in several scientific domains such as differential geometry theory, integrable quantum field theory, kink dynamics, and statistical mechanics. It makes more comprehensible the dynamics of strings and multi-strings in the constant curvature space. The current study has three main objectives. Examine the governing model to get novel solutions by employing the modified Kudryashov technique. Then compare it with the numerical technique of modified variational iteration method (MVIM) to calculate the error terms. Furthermore, employing bifurcation theory to produce a dynamical system. Additionally, use the dynamical system’s sensitivity analysis to investigate the model’s sensitivity. At last, for the validation of acquired results, the cryptography technique of novel image encryption and decryption is used. The research is greatly enhanced by the presentation of thorough 2D and 3D phase portraits. The field of mathematics and other sciences will benefit from these discoveries.

Strong Zero Modes in Integrable Quantum Circuits.

It is a classic result that certain interacting integrable spin chains host robust edge modes known as strong zero modes (SZMs). In this Letter, we extend this result to the Floquet setting of local quantum circuits, focusing on a prototypical model providing an integrable Trotterization for the evolution of the XXZ Heisenberg spin chain. By exploiting the algebraic structures of integrability, we show that an exact SZM operator can be constructed for these integrable quantum circuits in certain regions of parameter space. Our construction, which recovers a well-known result by Paul Fendley in the continuous-time limit, relies on a set of commuting transfer matrices known from integrability, and allows us to easily prove important properties of the SZM, including normalizabilty. Our approach is different from previous methods and could be of independent interest even in the Hamiltonian setting. Our predictions, which are corroborated by numerical simulations of infinite-temperature autocorrelation functions, are potentially interesting for implementations of the XXZ quantum circuit on available quantum platforms.

Unleashing the Power of Evolution in Xylanase Engineering: Investigating the Role of Distal Mutation Regulation.

The drive to enhance enzyme performance in industrial applications frequently clashes with the practical limitations of exhaustive experimental screening, underscoring the urgency for more refined and strategic methodologies in enzyme engineering. In this study, xylanase Xyl-1 was used as the model, coupling evolutionary insights with energy functions to obtain theoretical potential mutants, which were subsequently validated experimentally. We observed that mutations in the nonloop region primarily aimed at enhancing stability and also encountered selective pressure for activity. Notably, mutations in this region simultaneously boosted the Xyl-1 stability and activity, achieving a 65% success rate. Using a greedy strategy, mutant M4 was developed, achieving a 12 °C higher melting temperature and doubled activity. By integration of spectroscopy, crystallography, and quantum mechanics/molecular mechanics molecular dynamics, the mechanism behind the enhanced thermal stability of M4 was elucidated. It was determined that the activity differences between M4 and the wild type were primarily driven by dynamic factors influenced by distal mutations. In conclusion, the study emphasizes the pivotal role of evolution-based approaches in augmenting the stability and activity of the enzymes. It sheds light on the unique adaptive mechanisms employed by various structural regions of proteins and expands our understanding of the intricate relationship between distant mutations and enzyme dynamics.

Clarity in Wireless Quantum Communication: Exploring Explainable AI for Signal Modulation Classification

The advent of artificial intelligence (AI) and edge computing technologies has ushered in a new era for automatic modulation classification (AMC), with a particular focus on deep learning (DL)-based approaches. These AI-based AMC systems, deployed at edge devices, have shown remarkable advancements in recognizing and classifying a wide range of wireless signals. However, a significant challenge in this domain lies in the lack of adequate explanations for the models employed, which, in turn, hampers model accuracy and training efficiency. Consequently, the practical applications and further enhancements of these models are constrained. To address this limitation, researchers have started to explore interpretable methods for the technical analysis of DL-based AMC systems. In this paper, we delve into the subject, leveraging recent developments in interpretable methods, to provide a comprehensive review of applicable techniques and to outline the existing research challenges in the field of interpretable AMC. Moreover, we introduce a novel interpretable AI-based AMC framework designed to augment the interpretability of AMC outcomes. This framework achieves this by elucidating the contribution of wireless signal features to the training process of DL networks. In addition, we explore the potential impact of quantum computing on AMC systems. Quantum computing, with its ability to process complex computations at unprecedented speeds, offers a promising avenue for enhancing the efficiency and accuracy of AMC. By integrating quantum algorithms with AI-based AMC frameworks, it is possible to significantly improve the performance of wireless signal classification, especially in environments with high signal variability and noise. Our experimental results demonstrate that the proposed approach possesses the capacity to unravel the classification mechanisms hidden within opaque auto-modulated classification networks. Furthermore, it exhibits the potential to facilitate the training of networks on edge devices with reduced energy consumption and enhanced classification accuracy, thereby addressing critical challenges in the field of wireless signal classification. Additionally, the integration of quantum computing techniques holds the promise of further advancing the capabilities of AMC systems, paving the way for more robust and efficient wireless communication technologies.

Data-driven characterization of latent dynamics on quantum testbeds

This paper presents a data-driven approach to learn latent dynamics in superconducting quantum computing hardware. To this end, we augment the dynamical equation of quantum systems described by the Lindblad master equation with a parameterized source term that is trained from experimental data to capture unknown system dynamics, such as environmental interactions and system noise. We consider a structure preserving augmentation that learns and distinguishes unitary from dissipative latent dynamics parameterized by a basis of linear operators, as well as an augmentation given by a nonlinear feed-forward neural network. Numerical results are presented using data from two different quantum processing units (QPUs) at Lawrence Livermore National Laboratory's Quantum Device and Integration Testbed. We demonstrate that our interpretable, structure preserving, and nonlinear models are able to improve the prediction accuracy of the Lindblad master equation and accurately model the latent dynamics of the QPUs.

Microscopic Origin of the Quantum Mpemba Effect in Integrable Systems.

The highly complicated nature of far from equilibrium systems can lead to a complete breakdown of the physical intuition developed in equilibrium. A famous example of this is the Mpemba effect, which states that nonequilibrium states may relax faster when they are further from equilibrium or, put another way, hot water can freeze faster than warm water. Despite possessing a storied history, the precise criteria and mechanisms underpinning this phenomenon are still not known. Here, we study a quantum version of the Mpemba effect that takes place in closed many-body systems with a U(1) conserved charge: in certain cases a more asymmetric initial configuration relaxes and restores the symmetry faster than a more symmetric one. In contrast to the classical case, we establish the criteria for this to occur in arbitrary integrable quantum systems using the recently introduced entanglement asymmetry. We describe the quantum Mpemba effect in such systems and relate the properties of the initial state, specifically its charge fluctuations, to the criteria for its occurrence. These criteria are expounded using exact analytic and numerical techniques in several examples, a free fermion model, the Rule 54 cellular automaton, and the Lieb-Liniger model.

Quantum-Inspired Cryptography Protocols for Enhancing Security in Cloud Computing Infrastructures

As we know, cloud computing plays a vital role in our lives. It also plays a pivotal role in modern business and information technology landscapes. But with this, there is a rise in concerns regarding the security and privacy of all data which is stored in the cloud. To tackle these concerns some effective and traditional cryptographic methods are present but they face potential vulnerabilities due to advent of quantum computing. It also threatens the basis of widely used encryption algorithms and models. This research focuses on the usage of quantum mechanics inspired cryptographic protocols, which will help to strengthen the security of cloud computing models and infrastructures. The research begins with a detailed overview of the current situation and state of security of cloud computing. There is identification of all challenges and vulnerabilities faced due to current, classical and traditional cryptographic techniques and algorithms. As we know that there is a very close arrival of quantum computing, we are surrounded by mighty and latent threats because of quantum computing algorithms that can easily overcome the widely accepted and used encryption standards and models. So, there is a dire need to develop and implement some alternative cryptographic strategies and measures. To overcome these challenges, this research proposes the creation and usage of quantum-inspired cryptographic protocols which are designed to resist attacks from both traditional and quantum vulnerabilities. These protocols are inspired from quantum mechanics, like superposition and entanglement. These protocols will help to design and create cryptographic systems and models that offer enhanced security. The research focuses on the theoretical foundations of these quantum mechanics inspired protocols and assesses their practical feasibility within cloud computing infrastructures and environment.This research contains information regarding the challenges associated with integration and deployment of quantum inspired cryptographic solutions in cloud computing. It evaluates the scalability, efficiency, performance and computational overhead of these quantum inspired protocols to ensure their practical feasibility and capability in existing cloud computing environment and infrastructures. This research also includes comparison performed with quantum cryptographic protocols and traditional cryptographic methods. The results aim to provide evidence that quantum cryptographic techniques are better, feasible and secure options to protect data over cloud. In Conclusion, the research aims to provide an insight that development and usage of advanced security measures can withstand and handle evolving threats, ensuring the continued security and protection of data in cloud computing environment by providing theoretical insights, analysis and evolution.

Quantum computing in anthropological research: An interdisciplinary approach

This paper investigates the application of quantum computing in anthropological research. By leveraging quantum algorithms and computational capabilities, we propose innovative methodologies for analyzing complex cultural datasets, modeling social interactions, and reconstructing historical evolutionary patterns. The integration of quantum computing into anthropology has the potential to revolutionize the field by providing unprecedented computational efficiency and novel analytical tools.