Quantum Computing Algorithms Research Articles

Quantum algorithm for polaritonic chemistry based on an exact ansatz

Abstract Cavity-modified chemistry uses strong light-matter interactions to modify the electronic properties of molecules in order to enable new physical phenomena such as novel reaction pathways. As cavity chemistry often involves critical regions where configurations become nearly degenerate, the ability to treat multireference problems is crucial to understanding polaritonic systems. In this Letter, we show through the use of a unitary ansatz derived from the anti-Hermitian contracted Schrödinger equation that cavity-modified systems with strong correlation, such as the deformation of rectangular H4 coupled to a cavity mode, can be solved efficiently and accurately on a quantum device. In contrast, while our quantum algorithm can be made formally exact, classical-computing methods as well as other quantum-computing algorithms often yield answers that are both quantitatively and qualitatively incorrect. Additionally, we demonstrate the current feasibility of the algorithm on near intermediate-scale quantum hardware by computing the dissociation curve of H2 strongly coupled to a bosonic bath.

Application of Variational Quantum Eigensolver for Ground State Energies Calculation in Hydrogen and Helium Atomic Sequences

Exponential scaling presents a significant challenge in electronic structure calculations performed on classical computers. This paper explores how quantum computer algorithms can accurately represent quantum systems. Variational Quantum Eigensolver (VQE) algorithm is used to compute the ground state energy of hydrogen and helium sequences by implementing variational principle and quantum gates as trial wavefunction. This technique combines classical optimization with quantum computing calculations to simulate quantum systems on noisy and resource-limited computers. The resulting calculated energy is highly consistent to the corresponding exact values and Hartree-Fock calculations with a trend of when the number of atoms increases the calculated energy becomes more negative, leading to a decrease in the percentage error. Moreover, the convergence of the ground state energy of hydrogen and helium atoms was effectively optimized. The desired energy was reached, proven by adjusting the expectation value, and gradually achieving unity in state overlap. These findings demonstrate the VQE method's accuracy in calculating simple quantum systems and its scalability for larger atomic and molecular system, such as those in quantum chemistry and material science. However, challenges in quantum computer simulations, such as limited in qubit numbers and the presence of noise, require further advancements. Therefore, implementing a larger basis sets, advanced qubit mapping, specific chemistry ansatz, and flexible optimization techniques is one way to improve overall calculation.

Studying evaporating black hole using quantum computation algorithms on IBM quantum processor

Analyzing complex quantum systems using quantum computational algorithms is one of the most promising applications of quantum computers. This study focuses on evaluating the performance of a custom variational ansatz in the Variational Quantum Eigensolver (VQE) algorithm compared to predefined ansatzes. To achieve this, we employ the evaporating black hole model as a test bed for our analysis. Using the VQE approach, which integrates quantum and classical computing techniques, we aim to minimize the energy expectation value of the Hamiltonian. By training the circuit parameters of a trial wave function as a parameterized quantum circuit, we determine the upper bound for the ground state energy and assess the optimal variational form. We define a custom ansatz for the VQE protocol and compare its performance with other predefined ansatzes. Additionally, we test the performance of three different classical optimizers to further understand their impact on the VQE algorithm’s efficiency and accuracy.

On proving the robustness of algorithms for early fault-tolerant quantum computers

The hope of the quantum computing field is that quantum architectures are able to scale up and realize fault-tolerant quantum computing. Due to engineering challenges, such ''cheap'' error correction may be decades away. In the meantime, we anticipate an era of ''costly'' error correction, or early fault-tolerant quantum computing. Costly error correction might warrant settling for error-prone quantum computations. This motivates the development of quantum algorithms which are robust to some degree of error as well as methods to analyze their performance in the presence of error. Several such algorithms have recently been developed; what is missing is a methodology to analyze their robustness. To this end, we introduce a randomized algorithm for the task of phase estimation and give an analysis of its performance under two simple noise models. In both cases the analysis leads to a noise threshold, below which arbitrarily high accuracy can be achieved by increasing the number of samples used in the algorithm. As an application of this general analysis, we compute the maximum ratio of the largest circuit depth and the dephasing scale such that performance guarantees hold. We calculate that the randomized algorithm can succeed with arbitrarily high probability as long as the required circuit depth is less than 0.916 times the dephasing scale.

Quantum-inspired genetic algorithm for designing planar multilayer photonic structure

Quantum algorithms are emerging tools in the design of functional materials due to their powerful solution space search capability. How to balance the high price of quantum computing resources and the growing computing needs has become an urgent problem to be solved. We propose a novel optimization strategy based on an active learning scheme that combines the Quantum-inspired Genetic Algorithm (QGA) with machine learning surrogate model regression. Using Random Forests as the surrogate model circumvents the time-consuming physical modeling or experiments, thereby improving the optimization efficiency. QGA, a genetic algorithm embedded with quantum mechanics, combines the advantages of quantum computing and genetic algorithms, enabling faster and more robust convergence to the optimum. Using the design of planar multilayer photonic structures for transparent radiative cooling as a testbed, we show superiority of our algorithm over the classical genetic algorithm (CGA). Additionally, we show the precision advantage of the Random Forest (RF) model as a flexible surrogate model, which relaxes the constraints on the type of surrogate model that can be used in other quantum computing optimization algorithms (e.g., quantum annealing needs Ising model as a surrogate).

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.

Enhanced power system fault detection using quantum‐AI and herd immunity quantum‐AI fault detection with herd immunity optimisation in power systems

AbstractQuantum computing and deep learning have recently gained popularity across various industries, promising revolutionary advancements. The authors introduce QC‐PCSANN‐CHIO‐FD, a novel approach that enhances fault detection in electrical power systems by combining quantum computing, deep learning, and optimisation algorithms. The network, based on a Pyramidal Convolution Shuffle Attention Neural Network (PCSANN) optimised with the Coronavirus Herd Immunity Optimiser, shows promising results. Initially, historical datasets are used for fault detection. Preprocessing, which includes handling missing data and outliers using Adaptive Variational Bayesian Filtering is followed by Dual‐Domain Feature Extraction to extract grayscale statistical features. These features are processed by PCSANN to detect faults. The Coronavirus Herd Immunity Optimisation Algorithm is proposed to optimise PCSANN for precise fault detection. Performance of the proposed QC‐PCSANN‐CHIO‐FD approach attains 24.11%, 28.56% and 22.73% high specificity, 21.89%, 23.04% and 9.51% lower computation Time, 25.289%, 15.35% and 19.91% higher ROC and 8.65%, 13.8%, and 7.15% higher Accuracy compared with existing methods, such as combining deep learning based on quantum computing for electrical power system malfunction diagnosis (QC‐ANN‐FD), electrical power system fault diagnostics using hybrid quantum‐classical deep learning (QC‐CRBM‐FD), applications of machine learning to the identification of power system faults: Recent developments and future directions (QC‐RF‐FD).

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.

Blockchain-based Device Authentication in Edge Computing using Quantum Approach

The Internet of things (IoT) is emerged as a new technology where everything is connected. Large amount of data need to be stored for processing; hence, edge computing can reduce the storage of data in a distributed environment, which enhances processing speed and low usage of bandwidth. With an ever increasing use of IoT devices, issues such as authentication of devices, privacy of data stored, and integrity of data have also increased. The authentication of devices is a major concern for edge-connected IoT devices. The problem was solved by using classical cryptographic algorithms such as Elliptic Curve Cryptography (ECC), Rivest-Shamir-Adleman (RSA), and Diffie-Hellman (DH) for message encryption by using public and private keys that need to be stored. These keys need to be stored on a server for device authentication. In device authentication, storing many keys leads to more computation and storage costs and also increase in delay. With quantum computing and quantum algorithms such as Shor’s and Grover’s, it becomes easy to break the keys of cryptographic algorithms, making the system vulnerable. The proposed work Blockchain based Device Authentication in Edge Computing using Quantum Approach (BDAEC-QA) provides authentication for IoT devices using it’s context information, quantum key distribution (QKD) and blockchain. The proposed scheme uses the smart contracts to store an information of the IoT devices on the server side, which is used by blockchain to provide secure authentication between the edge server and the IoT devices. The proposed scheme also provides communication between IoT devices across the network. The proposed work is compared with “Lightweight Two-Factor-Based User Authentication Protocol for IoT-Enabled Healthcare Ecosystem in Quantum Computing" (LTBA), and “A Blockchain-Based Mutual Authentication Scheme for Collaborative Edge Computing" (BBMA), and has less registration, key generation and authentication delay respectively. The BDAEC-QA scheme uses less computation and storage costs as compared with other existing schemes. The proposed scheme is simulated using the AVISPA tool, to provide the security proofs and analysis that indicate BDAEC-QA scheme is resistant to well-known attacks.

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