Quantum Computing Algorithms Research Articles

Exploration and Development of Quantum Computing Algorithms for Optimization, Cryptography, and Machine Learning Applications

Quantum computing, with its potential to revolutionize computation, relies fundamentally on the development of efficient algorithms to leverage its unparalleled processing capabilities. This research delves into the creation, exploration, and refinement of quantum computing algorithms, focusing on their applications in optimization, cryptography, and machine learning. Quantum algorithms such as Shor's and Grover's have demonstrated remarkable advantages in factorization and search problems, while more recent innovations are tackling complex challenges in global optimization and data analysis. By integrating principles of quantum mechanics—such as superposition, entanglement, and interference—these algorithms promise exponential speed-ups over classical counterparts in specific domains. This study critically analyzes existing quantum algorithms, proposes advancements in hybrid quantum-classical frameworks, and explores their implications for practical problem-solving. Through simulations and theoretical evaluations, it aims to bridge the gap between quantum theory and real-world applications, contributing to the evolution of quantum computing as a transformative technology.

Quantum Neural Networks: A New Frontier

Abstract. In recent years, there has been remarkable progress in improving the availability of resources and refining algorithms for quantum computing. Since the late 1980s, the scientific community has been fascinated by the idea of harnessing quantum phenomena to tackle computational problems. This article provides a comprehensive exploration of the foundational theories and practical applications of quantum neural networks (QNNs), highlighting their potential to transform machine learning through unique features like quantum parallelism and entanglement. It delves into various QNN architectures, such as quantum circuits and hybrid quantum-classical models, showcasing their effectiveness in handling intricate computational tasks more efficiently than traditional neural networks. Furthermore, the article examines the current challenges and future prospects in this rapidly advancing field, emphasizing the pivotal role of QNNs in driving forward research in both quantum computing and artificial intelligence. Quantum neural networks are poised to not only enhance computational capabilities but also pave the way for groundbreaking innovations in diverse technological domains.

Investigating the Impact of Quantum Computing on Algorithmic Complexity

This paper investigated the transformation that quantum computing brought into algorithmic complexity in the theoretical setting of computer science. This involved the appearance of new paradigm changes brought forth by quantum technologies, imposing on a glance at the performance of quantum algorithms in respect to classical models of computation regarding their effectiveness. Our contributions encompassed key quantum algorithms, specifically Shor's and Grover's algorithms, underlining the performance metrics of those algorithms. The mathematical modeling was supported by simulations using python libraries like Qiskit, which helped analyze the complexities of both algorithm types. From our simulations, it emerged that for smaller sizes of input, classical algorithms executed faster and illustrated their established efficiency. In contrast, quantum computing-algorithms like Grover's and Shor's - performed so much better for larger input sizes, showing potential advantages that may change the face of computational limitations. While promising much, it seemed from our findings that quantum computing would not show a quantum advantage for all computational tasks, because classical algorithms still remained robust and effective for many scenarios. This nuanced understanding underlines how complementary both the classical and quantum approaches are. Therefore, the insights gained through this work provide the basis for investigating where boundaries of computational capabilities evolve and what practical implications are of the integration of quantum technologies into existing systems.

U(1) fields from qubits: An approach via D-theory algebra

A new quantum link microstructure was proposed for the lattice quantum chromodynamics (QCD) Hamiltonian, replacing the Wilson gauge links with a bilinear of fermionic qubits, later generalized to D-theory. This formalism provides a general framework for building lattice field theory algorithms for quantum computing. We focus mostly on the simplest case of a quantum rotor for a single compact U(1) field. We also make some progress for non-Abelian setups, making it clear that the ideas developed in the U(1) case extend to other groups. These in turn are building blocks for 1+0-dimensional (1+0-D) matrix models, 1+1-D sigma models and non-Abelian gauge theories in 2+1 and 3+1 dimensions. By introducing multiple flavors for the U(1) field, where the flavor symmetry is gauged, we can efficiently approach the infinite-dimensional Hilbert space of the quantum O(2) rotor with increasing flavors. The emphasis of the method is on preserving the symplectic algebra exchanging fermionic qubits by sigma matrices (or hard bosons) and developing a formal strategy capable of generalization to a SU(3) field for lattice QCD and other non-Abelian 1+1-D sigma models or 3+1-D gauge theories. For U(1), we discuss briefly the qubit algorithms for the study of the discrete 1+1-D sine-Gordon equation. Published by the American Physical Society 2024

Development of quantum computing algorithm of technology for monitoring learning results

The present publication considers implementing an online control proctoring system, with the possibility of using methods and models of pattern recognition using algorithmic quantum computing to conduct online exams. The study's object is the protection method within infrastructure proctoring systems in education. The study aims to create a security system for proctoring technology infrastructure in education. The article proposes an alternative approach to building protection systems with an effective recognition model using algorithmic quantum computing in proctoring platforms. This study addresses these issues and proposes a novel approach to generating a random cryptographic key using multimodal biometric technology. A presented quantum algorithm method for computer simulation of the data processing quantum principles allows studying and analysing how the created model for transforming a classical image into a quantum state works. This method also shows the possibilities of quantum information theory in interpreting classical problems or how to optimise the same, taking into account the development of methods for the functioning of models and algorithms for quantum computing, data protection and security of online video communications in a proctoring system in an educational environment. The novelty of this research is expressed primarily in the constant updating and addition of authentication systems using quantum computing in various aspects, including the proctoring system in the educational environment. Also, scientific novelty is associated with insufficient similar research in the information space. The practical significance is due to the need in the current situation to attract attention to existing problems in structuring the infrastructure of a monitoring system within planning and coordinating the protection, thereby enhancing learning outcomes by eliminating security flaws using a quantum computing algorithm for pattern recognition

A recurrent Gaussian quantum network for online processing of quantum time series

Over the last decade, researchers have studied the interplay between quantum computing and classical machine learning algorithms. However, measurements often disturb or destroy quantum states, requiring multiple repetitions of data processing to estimate observable values. In particular, this prevents online (real-time, single-shot) processing of temporal data as measurements are commonly performed during intermediate stages. Recently, it was proposed to sidestep this issue by focusing on tasks with quantum output, eliminating the need for detectors. Inspired by reservoir computers, a model was proposed where only a subset of the internal parameters are trained while keeping the others fixed at random values. Here, we also process quantum time series, but we do so using a Recurrent Gaussian Quantum Network (RGQN) of which all internal interactions can be trained. As expected, this increased flexibility yields higher performance in benchmark tasks. Building on this, we show that the RGQN can tackle two quantum communication tasks, while also removing some hardware restrictions of the currently available methods. First, our approach is more resource efficient to enhance the transmission rate of quantum channels that experience certain memory effects. Second, it can counteract similar memory effects if they are unwanted, a task that could previously only be solved when redundantly encoded input signals could be provided. Finally, we run a small-scale version of the last task on Xanadu’s photonic processor Borealis.

Quantum Computing Algorithms for Integer Factorization: A Comparative Analysis

Quantum Computing Algorithms for Integer Factorization: A Comparative Analysis

Cost-aware quantum-inspired genetic algorithm for workflow scheduling in hybrid clouds

Cloud computing delivers a desirable environment for users to run their different kinds of applications in a cloud. Numerous of these applications (tasks), such as bioinformatics, astronomy, biodiversity, and image analysis, are deadline-sensitive. Such tasks must be properly allocated to virtual machines (VMs) to avoid deadline violations, and they should reduce their execution time and cost. Due to the contradictory environment, minimizing the application task's completion time and execution cost is extremely difficult. Thus, we propose a Cost-aware Quantum-inspired Genetic Algorithm (CQGA) to minimize the execution time and cost by meeting the deadline constraints. CQGA is motivated by quantum computing and genetic algorithm. It combines quantum operators (measure, interference, and rotation) with genetic operators (selection, crossover, and mutation). Quantum operators are used for better population diversity, quick convergence, time-saving, and robustness. Genetic operators help to produce new individuals, have good fitness values for individuals, and play a significant role in preserving the evolution quality of the population. In addition, CQGA used a quantum bit as a probabilistic representation because it has higher population diversity attributes than other representations. The simulation outcome exhibits that the proposed algorithm can obtain outstanding convergence performance and reduced maximum cost than benchmark algorithms.

Quantum Computing Algorithms for Nonlinear Optimization Problems

The increasing complexity of real-world optimization problems highlights the importance of this research since classical algorithms are unable to provide efficient answers in these cases. Innovative methods for fast and scalable resolution of nonlinear optimization problems are required because these problems are prevalent in many fields. The potential for quantum computing to speed up optimization processes and overcome classical limitations is great, owing to its superposition principles and intrinsic parallelism. The integration of quantum algorithms (I-QA) into real-world applications, however, will not always be smooth sailing. There are significant challenges associated with preserving quantum coherence, correcting errors, and working within hardware limits. To enable the simultaneous exploration of solution spaces through quantum parallelism, this research proposes the Hybrid Quantum Gradient -Classical Approach (HQG-CA), which makes use of parameterized quantum circuits to represent probable solutions. Additionally, improves convergence rates through applying quantum gradient information to direct optimization in the quantum state space. Optimization of portfolios in finance, adjustment of model parameters in machine learning, and optimization of routes in logistics are a few examples of the many industries that find use for HQG-CA. These applications are explored in this abstract, which highlights the revolutionary potential of HQG-CA to solve optimization problems in the real world. The effectiveness of HQG-CA is assessed through a thorough simulation experiment. Performance measures such algorithmic speedup, solution accuracy, and scalability are discussed, which is based on extensive testing and comparison with classical alternatives. The present research provides a comprehensive evaluation of HQG-CA's potential for tackling nonlinear optimization problems.

Quantum Computing Algorithms for Solving Complex Mathematical Problems

The power of quantum mechanics, that is too complex for conventional computers, can be solved by an innovative model of computing known as quantum computing. Quantum algorithms can provide exponential speedups for some types of problems, such as many difficult mathematical ones. In this paper, we review some of the most important quantum algorithms for hard mathematical problems. When factoring large numbers, Shor's algorithm is orders of magnitude faster than any other known classical algorithm. The Grover's algorithm, which searches unsorted databases much more quickly than conventional algorithms, is then discussed.

Weight Optimization of Discrete Truss Structures Using Quantum-Based HS Algorithm

Recently, a new field that combines metaheuristic algorithms and quantum computing has been created and is being applied to optimization problems in various fields. However, the application of quantum computing-based metaheuristic algorithms to the optimization of structural engineering is insufficient. Therefore, in this paper, we tried to optimize the weight of the truss structure using the QbHS (quantum-based harmony search) algorithm, which combines quantum computing and conventional HS (harmony search) algorithms. First, the convergence performance according to the parameter change of the QbHS algorithm was compared. The parameters selected for the comparison of convergence performance are QHMS, QHMCR, QPAR, ϵ, and θr. The selected parameters were compared using six benchmark functions, and the range for deriving the optimal convergence performance was found. In addition, weight optimization was performed by applying it to a truss structure with a discrete cross-sectional area. The QbHS algorithm derived a lower weight than the QEA (quantum-inspired evolutionary algorithm) and confirmed that the convergence performance was better. A new algorithm that combines quantum computing and metaheuristic algorithms is required for application to various engineering problems, and this effort is essential for the expansion of future algorithm development.

Efficient Application of the Factorized form of the Unitary Coupled-Cluster Ansatz for the Variational Quantum Eigensolver Algorithm by Using Linear Combination of Unitaries

The variational quantum eigensolver is one of the most promising algorithms for near-term quantum computers. It has the potential to solve quantum chemistry problems involving strongly correlated electrons with relatively low-depth circuits, which are otherwise difficult to solve on classical computers. The variational eigenstate is constructed from a number of factorized unitary coupled-cluster terms applied onto an initial (single-reference) state. Current algorithms for applying one of these operators to a quantum state require a number of operations that scale exponentially with the rank of the operator. We exploit a hidden SU(2) symmetry to allow us to employ the linear combination of unitaries approach, Our Prepare subroutine uses n+2 ancilla qubits for a rank-n operator. Our Select(U^) scheme uses O(n)Cnot gates. This results in a full algorithm that scales like the cube of the rank of the operator n3, a significant reduction in complexity for rank five or higher operators. This approach, when combined with other algorithms for lower-rank operators (when compared to the standard implementation), will make the factorized form of the unitary coupled-cluster approach much more efficient to implement on all types of quantum computers.

Development of an improved SSL/TLS protocol using post-quantum algorithms

The development of Internet technologies together with mobile and computer technologies have formed smart technologies that allow the formation of both cyber-physical and socio-cyber-physical systems. The basis of smart technologies is the integration of wireless channel standards with mobile and computer protocols. 4G/5G technologies are integrated with various web platforms, taking into account the digitalization of services in cyberspace. But the SSL/TLS protocol, based on the hybridization of symmetric encryption algorithms with hashing algorithms (AEAD mode), which is supposed to provide security services, is vulnerable to “Meet in the middle”, POODLE, BEAST, CRIME, BREACH attacks. In addition, with the advent of a full-scale quantum computer, symmetric and asymmetric cryptography algorithms that provide security services can also be hacked. To increase the level of security, an improved protocol based on post-quantum algorithms – crypto-code constructions is proposed, which will ensure not only resistance to current attacks, but also stability in the post-quantum period. To ensure the “hybridity” of services, it is proposed to use the McEliece and Niederreiter crypto-code constructions (confidentiality and integrity are ensured) and the improved UMAC algorithm on the McEliece crypto-code construction. Taking into account the level of “secrecy” of information, it is suggested to use various combinations of crypto-code constructions on different algebraic geometric and/or flawed codes. The use of crypto-code constructions not only provides resistance to attacks, but also simplifies the formation of a connection – the parameters of elliptic curves are used to transmit a common key. This approach significantly reduces the connection time of mobile gadgets and simplifies the procedure of agreement before data transfer

Interpreting Housing Prices with a MultidisciplinaryApproach Based on Nature-Inspired Algorithms and Quantum Computing

Current technology still does not allow the use of quantum computers for broader and individual uses; however, it is possible to simulate some of its potentialities through quantum computing. Quantum computing can be integrated with nature-inspired algorithms to innovatively analyze the dynamics of the real estate market or any other economic phenomenon. With this main aim, this study implements a multidisciplinary approach based on the integration of quantum computing and genetic algorithms to interpret housing prices. Starting from the principles of quantum programming, the work applies genetic algorithms for the marginal price determination of relevant real estate characteristics for a particular segment of Naples’ real estate market. These marginal prices constitute the quantum program inputs to provide, as results, the purchase probabilities corresponding to each real estate characteristic considered. The other main outcomes of this study consist of a comparison of the optimal quantities for each real estate characteristic as determined by the quantum program and the average amounts of the same characteristics but relative to the real estate data sampled, as well as the weights of the same characteristics obtained with the implementation of genetic algorithms. With respect to the current state of the art, this study is among the first regarding the application of quantum computing to interpretation of selling prices in local real estate markets.

A Dynamic Image Encryption Scheme Based on Quantum Walk and Chaos-Induced DNA

The development of quantum information technology and increasing attention of people to the secure transmission of image information in the Internet have put forward higher requirements for traditional image encryption algorithms that not only take advantage of the exponential acceleration ability of quantum computing compared with classical computing but also reduce the risk of encryption algorithms being cracked. Therefore, in order to seek the combination of the advantages of quantum computing and classical image encryption algorithms, this paper proposes a new dynamic encryption image scheme of quantum walk and chaos-induced DNA. Firstly, the RGB three-channel pixels of the color image are extracted and combined into a one-dimensional array, and a random sequence is generated by quantum walk to reorder it to obtain a preliminary scrambled image; secondly, the color image is processed by the SHA-256 algorithm and divided into the generated message digest as the initial condition of the chaotic model. The random sequence was generated by the high-dimensional chaotic model which encodes each pixel independently and disorderly as DNA bases. The difference of the chaotic sequence ensures the dynamic selection of random DNA encoding and decoding rules during encryption. At the same time, the number of times of DNA encryption of the encoded pixel value is also controlled by the dynamic induction of the chaotic sequence, and ultimately, the DNA coding sequence is replaced with the decimal pixel value to obtain the encrypted image. The simulation results show that the information entropy of the encrypted image is above 7.99, and the correlation of each channel is close to 0, which can effectively resist brute force attacks, plaintext attacks, statistical analysis attacks, noise attacks, etc. In addition, in this paper, extracting the watermark embedded in the encrypted image to judge whether image information is tampered or forged further improves the security of the image information.

Size and Topology Optimization of Truss Structures Using Quantum-Based HS Algorithm

With the development of various metaheuristic algorithms, research cases that perform weight optimization of truss structures are steadily progressing. In particular, due to the possibility of developing quantum computers, metaheuristic algorithms combined with quantum computation are being developed. In this paper, the QbHS (Quantum based Harmony Search) algorithm was proposed by combining quantum computation and the conventional HS (Harmony Search) algorithms, and the size and topology optimization of the truss structure was performed. The QbHS algorithm has the same repetitive computational structure as the conventional HS algorithm. However, the QbHS algorithm constructed QHM (Quantum Harmony Memory) using the probability of Q-bit and proposed to perform pitch adjusting using the basic state of Q-bit. To perform weight optimization of truss structures using the proposed QbHS algorithm, 20 bar, 24 bar, and 72-bar truss structures were adopted as examples and compared with the results of the QE (Quantum Evolutionary) algorithm. As a result, it was confirmed that the QbHS algorithm had excellent convergence performance by finding a lower weight than the QE algorithm. In addition, by expressing the weight optimization results of the truss structure with an image coordinate system, the topology of the truss structure could be confirmed only by the picture. The results of this study are expected to play an important role in future computer information systems by combining quantum computation and conventional HS algorithms.

Measurement Optimization Techniques for Excited Electronic States in Near-Term Quantum Computing Algorithms.

The variational quantum eigensolver (VQE) remains one of the most popular near-term quantum algorithms for solving the electronic structure problem. Yet, for its practicality, the main challenge to overcome is improving the quantum measurement efficiency. Numerous quantum measurement techniques have been developed recently, but it is unclear how these state-of-the-art measurement techniques will perform in extensions of VQE for obtaining excited electronic states. Assessing the measurement techniques' performance in the excited state VQE is crucial because the measurement requirements in these extensions are typically much greater than in the ground state VQE, as one must measure the expectation value of multiple observables in addition to that of the electronic Hamiltonian. Here, we adapt various measurement techniques to two widely used excited state VQE algorithms: multistate contraction and quantum subspace expansion. Then, the measurement requirements of each measurement technique are numerically compared. We find that the best methods for multistate contraction are ones utilizing Hamiltonian data and wave function information to minimize the number of measurements. In contrast, randomized measurement techniques are more appropriate for quantum subspace expansion, with many more observables of vastly different energy scales to measure. Nevertheless, when the best possible measurement technique for each excited state VQE algorithm is considered, significantly fewer measurements are required in multistate contraction than in quantum subspace expansion.

Security of Neural Network-Based Key Agreement Protocol for Smart Grids

Recent developments in quantum computing pose a significant threat to the asymmetric cryptography currently in use. Neural cryptography offers a potential alternative that is resistant to attacks of known quantum computer algorithms. The considered solution is lightweight and computationally efficient. If a quantum computer algorithm were successfully implemented, it could expose IoT sensors and smart grid components to a wide range of attack vectors. Given the lightweight nature of neural cryptography and the potential risks, neural cryptography could have potential applications in both IoT sensors and smart grid systems. This paper evaluates one of the suggested enhancements: the use of integer-valued input vectors that accelerate the synchronization of the Tree Parity Machine. This enhancement introduces a new parameter M that indicates the minimum and maximum values of input vector elements. This study evaluates the nonbinary version of the mutual learning algorithm in a simulated insecure environment. The results indicate that, while the Nonbinary Tree Parity Machine may involve some trade-offs between security and synchronization time, the speed improvement is more substantial than the decrease in security. The impact of this enhancement is particularly significant for smaller adjustments to parameter M.

OVERVIEW OF CANDIDATES FOR QUANTUM-RESISTANT CIPHERS

This article describes the main trends in the development of cryptography, in particular, the need for active research in the field of postquantum cryptography. The purpose of the article was to review the latest trends in the field of post-quantum cryptography, due to the emergence of quantum algorithms, in order to reflect the current problems arising in the field of modern cryptography. The main method of research is the analysis of scientific literature for the period from 2016 to 2022. The use of quantum computer and quantum algorithms will significantly reduce the time of cracking keys with encryption and solve some types of cryptographic hash functions, which will lead to a significant increase in the length of keys and a decrease in performance. Due to the great economic influence of the USA, it is necessary to pay attention to the post–quantum NIST contests: from the algorithms under consideration, lattice-based algorithms will be standardized, which are the most reliable and efficient in terms of performance according to NIST, however, in order not to rely only on this type of algorithms, NIST selected alternative algorithms–isogeny–based, code–based, hash–based. So, there is a need to conduct research on the search for post-quantum algorithms of various types, which is confirmed by various NIST competitions. Post-quantum algorithms based on the computational difficulty of solving systems of many quadratic equations with many variables are also effective, such algorithms have not been considered by NIST, but they are relevant for further research. Since updating protocols, schemes and infrastructure objects must be carried out together with the introduction of new cryptographic algorithms, the replacement of currently used cryptographic algorithms can be very destructive and take decades, re-encryption with such a new algorithm of stored information and keys can also be used.

The effect of superposition and entanglement on hybrid quantum machine learning for weather forecasting

Recently, proposed algorithms for quantum computing and generated quantum computer technologies continue to evolve. On the other hand, machine learning has become an essential method for solving many problems such as computer vision, natural language processing, prediction and classification. Quantum machine learning is a new field developed by combining the advantages of these two primary methods. As a hybrid approach to quantum and classical computing, variational quantum circuits are a form of machine learning that allows predicting an output value against input variables. In this study, the effects of superposition and entanglement on weather forecasting, were investigated using a variational quantum circuit model when the dataset size is small. The use of the entanglement layer between the variational layers has made significant improvements on the circuit performance. The use of the superposition layer before the data encoding layer resulted in the use of less variational layers.