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Quantum chemistry is one of the most promising applications for which quantum computing is expected to have a significant impact. Despite considerable research in the field of electronic structure, calculating the vibrational properties of molecules on quantum computers remains a relatively unexplored field. In this work, we develop a vibrational Adaptive Derivative-Assembled Pseudo-Trotter Variational Quantum Eigensolver (vADAPT-VQE) formalism based on an infinite product representation (IPR) of anti-Hermitian excitation operators of the Full Vibrational Configuration Interaction (FVCI) wavefunction, which allows for preparing eigenstates of vibrational Hamiltonians on quantum computers. In order to establish the vADAPT-VQE algorithm using the IPR, we study the exactness of disentangled Unitary Vibrational Coupled Cluster (dUVCC) theory and show that dUVCC can formally represent the FVCI wavefunction in an infinite expansion. To investigate the performance of the vADAPT-VQE algorithm, we numerically study whether the vADAPT-VQE algorithm generates a sequence of operators that may represent the FVCI wavefunction. Our numerical results indicate frequent appearance of critical points in the wavefunction preparation using vADAPT-VQE. These results imply that one may encounter diminishing usefulness when preparing vibrational wavefunctions on quantum computers using vADAPT-VQE and that additional studies are required to find methods that can circumvent this behavior. [ABSTRACT FROM AUTHOR]

The recently developed Projective Quantum Eigensolver (PQE) offers an elegant procedure to evaluate the ground state energies of molecular systems in quantum computers. However, the noise in available quantum hardware can result in significant errors in computed outcomes, limiting the realization of quantum advantage. Although PQE comes equipped with some degree of inherent noise resilience, any practical implementation with apposite accuracy would require additional routines to eliminate or mitigate the errors further. In this work, we propose a way to enhance the efficiency of PQE by developing an optimal framework for introducing Zero Noise Extrapolation (ZNE) in the nonlinear iterative procedure that outlines the PQE, leading to the formulation of ZNE-PQE. Moreover, we perform a detailed analysis of how various components involved in it affect the accuracy and efficiency of the reciprocated energy convergence trajectory. Additionally, we investigate the underlying mechanism that leads to the improvements observed in ZNE-PQE over conventional PQE by performing a comparative analysis of their residue norm landscape. This approach is expected to facilitate practical applications of quantum computing in fields related to molecular sciences, where it is essential to determine molecular energies accurately. [ABSTRACT FROM AUTHOR]

The limited capabilities of current quantum hardware significantly constrain the scale of experimental demonstrations of most quantum algorithmic primitives. This makes it challenging to perform benchmarking of the current hardware using useful quantum algorithms, i.e., application-oriented benchmarking. In particular, the Harrow-Hassidim-Lloyd (HHL) algorithm is a critical quantum linear algebra primitive, but the majority of the components of HHL are far out of the reach of noisy intermediate-scale quantum devices, which has led to the proposal of hybrid classical-quantum variants. The goal of this work is to further bridge the gap between proposed near-term friendly implementations of HHL and the kinds of quantum circuits that can be executed on noisy hardware. Our proposal adds to the existing literature of hybrid quantum algorithms for linear algebra that are more compatible with the current scale of quantum devices. Specifically, we propose two modifications to the Hybrid HHL algorithm proposed by Lee et al., leading to our algorithm Hybrid HHL + + : (1) propose a novel algorithm for determining a scaling factor for the linear system matrix that maximizes the utility of the amount of ancillary qubits allocated to the phase estimation component of HHL, and (2) introduce a heuristic for compressing the HHL circuit. We demonstrate the efficacy of our work by running our modified Hybrid HHL on Quantinuum System Model H-series trapped-ion quantum computers to solve different problem instances of small-scale portfolio optimization problems, leading to the largest experimental demonstrations of HHL for an application to date. [ABSTRACT FROM AUTHOR]

The limited capabilities of current quantum hardware significantly constrain the scale of experimental demonstrations of most quantum algorithmic primitives. This makes it challenging to perform benchmarking of the current hardware using useful quantum algorithms, i.e., application-oriented benchmarking. In particular, the Harrow-Hassidim-Lloyd (HHL) algorithm is a critical quantum linear algebra primitive, but the majority of the components of HHL are far out of the reach of noisy intermediate-scale quantum devices, which has led to the proposal of hybrid classical-quantum variants. The goal of this work is to further bridge the gap between proposed near-term friendly implementations of HHL and the kinds of quantum circuits that can be executed on noisy hardware. Our proposal adds to the existing literature of hybrid quantum algorithms for linear algebra that are more compatible with the current scale of quantum devices. Specifically, we propose two modifications to the Hybrid HHL algorithm proposed by Lee et al., leading to our algorithm Hybrid HHL + + : (1) propose a novel algorithm for determining a scaling factor for the linear system matrix that maximizes the utility of the amount of ancillary qubits allocated to the phase estimation component of HHL, and (2) introduce a heuristic for compressing the HHL circuit. We demonstrate the efficacy of our work by running our modified Hybrid HHL on Quantinuum System Model H-series trapped-ion quantum computers to solve different problem instances of small-scale portfolio optimization problems, leading to the largest experimental demonstrations of HHL for an application to date. [ABSTRACT FROM AUTHOR]

Variational quantum algorithms represent a powerful approach for solving optimization problems on noisy quantum computers, with a broad spectrum of potential applications ranging from chemistry to machine learning. However, their performances in practical implementations crucially depend on the effectiveness of quantum circuit training, which can be severely limited by phenomena such as barren plateaus. While, in general, dissipation is detrimental for quantum algorithms, and noise itself can actually induce barren plateaus, here we describe how the inclusion of properly engineered Markovian losses after each unitary quantum circuit layer allows for the trainability of quantum models. We identify the required form of the dissipation processes and establish that their optimization is efficient. We benchmark the generality of our proposal in both a synthetic and a practical quantum chemistry example, demonstrating its effectiveness and potential impact across different domains. [ABSTRACT FROM AUTHOR]

We design a quantum method for classical information compression that exploits the hidden subgroup quantum algorithm. We consider sequence data in a database with a priori unknown symmetries of the hidden subgroup type. We prove that data with a given group structure can be compressed with the same query complexity as the hidden subgroup problem, which is exponentially faster than the best-known classical algorithms. We moreover design a quantum algorithm that variationally finds the group structure and uses it to compress the data. There is an encoder and a decoder, along the paradigm of quantum autoencoders. After the training, the encoder outputs a compressed data string and a description of the hidden subgroup symmetry, from which the input data can be recovered by the decoder. In illustrative examples, our algorithm outperforms the classical autoencoder on the mean squared value of test data. This classical-quantum separation in information compression capability has thermodynamical significance: the free energy assigned by a quantum agent to a system can be much higher than that of a classical agent. Taken together, our results show that a possible application of quantum computers is to efficiently compress certain types of data that cannot be efficiently compressed by current methods using classical computers. [ABSTRACT FROM AUTHOR]

Linear systems of equations lie at the heart of numerous scientific and engineering challenges. In cutting-edge arena like artificial intelligence, machine learning and neuro-computation, these systems serve as a fundamental tool for mathematical modeling. Classical algorithms for solving linear systems have been extensively developed and forms the backbone of diverse applications across various scientific disciplines. While classical algorithms exist for solving linear systems, they often encounter limitations termed “NP-completeness” as data complexity increases. The emerging field of quantum computing offers a revolutionary approach to deal with these kinds of problems. The Harrow–Hassidim–Lloyd (HHL) algorithm tackles these challenges and opens new avenues for research. This study delves into the contemporary effectiveness of the HHL algorithm to address systems of linear equations. By examining recent research in quantum machine learning, we aim to assess the HHL algorithm’s potential to revolutionize the process of optimizing hyperparameters for machine learning models, resulting in increased efficiency and cost savings. This paper meticulously analyzes the HHL algorithm and explores its evolution from conception to the latest advancements. A comprehensive examination of the HHL algorithm, including its evolution over time, is thoroughly explored. The investigation delves into the potential challenges and limitations that might hinder the practical deployment of the HHL algorithm. Identifying these roadblocks will pave the way for future research and development efforts. [ABSTRACT FROM AUTHOR]

Recent rank-based attacks have reduced the security of Rainbow, which is one of the multi-layer UOV signatures, below the NIST security requirements by speeding up iterative kernel-finding operations using classical mathematics techniques. If quantum algorithms are applied to perform these iterative operations, the rank-based attacks may be more threatening to multi-layer UOV, including Rainbow. In this paper, we propose a quantum rectangular MinRank attack called the Q-rMinRank attack, the first quantum approach to key recovery attacks on multi-layer UOV signatures. Our attack is a general model applicable to multi-layer UOV signature schemes, and in this paper, we provide examples of its application to Rainbow and the Korean TTA standard, HiMQ. We design two quantum oracle circuits to find the kernel in consideration of the depth-width trade-off of quantum circuits. One is to reduce the width of the quantum circuits using qubits as a minimum, and the other is to reduce the depth using parallelization instead of using a lot of qubits. By designing quantum circuits to find kernels with fewer quantum resources and complexity by adding mathematical techniques, we achieve quadratic speedup for the MinRank attack to recover the private keys of multi-layer UOV signatures. We also estimate quantum resources for the designed quantum circuits and analyze quantum complexity based on them. The width-optimized circuit recovers the private keys of Rainbow parameter set V with only 1089 logical qubits. The depth-optimized circuit recovers the private keys of Rainbow parameter set V with a quantum complexity of 2 174 , which is lower than the complexity of 2 221 recovering the secret key of AES-192, which provides the same security level as parameter set III. [ABSTRACT FROM AUTHOR]

Quantum walks are referred to as quantum analogs to random walks in mathematics. They have been studied as quantum algorithms in quantum information for quantum computers. There are two types of quantum walks. One is the discrete-time quantum walk and the other is the continuous-time quantum walk. We study a continuous-time quantum walk on the half line and challenge to find a limit theorem for it in this paper. As a result, approximate behavior of the quantum walker is revealed after the system of quantum walk gets updated in long time. [ABSTRACT FROM AUTHOR]

The development of a universal fault-tolerant quantum computer that can solve efficiently various difficult computational problems is an outstanding challenge for science and technology. In this work, we propose a technique for an efficient implementation of quantum algorithms with multilevel quantum systems (qudits). Our method uses a transpilation of a circuit in the standard qubit form, which depends on the characteristics of a qudit-based processor, such as the number of available qudits and the number of accessible levels. This approach provides a qubit-to-qudit mapping and comparison to a standard realization of quantum algorithms highlighting potential advantages of qudits. We provide an explicit scheme of transpiling qubit circuits into sequences of single-qudit and two-qudit gates taken from a particular universal set. We then illustrate our method by considering an example of an efficient implementation of a 6-qubit quantum algorithm with qudits. In this particular example, we demonstrate how using qudits allows a decreasing amount of two-body interactions in the qubit circuit implementation. We expect that our findings are of relevance for ongoing experiments with noisy intermediate-scale quantum devices that operate with information carriers allowing qudit encodings, such as trapped ions and neutral atoms, as well as optical and solid-state systems. [ABSTRACT FROM AUTHOR]

Summary: As the demand for cloud storage systems increases, ensuring the security and integrity of cloud data becomes a challenge. Data uploaded to cloud systems are vulnerable to numerous sorts of assaults, which must be handled appropriately to avoid data tampering issues. In addition, quantum computers are expected to be introduced soon, which may face multiple security issues by destroying all traditional cryptosystems. This work introduces a quantum‐resistant blockchain centered data integrity verification system with the use of several techniques. Initially, the keys and signatures are generated by the users with the help of the lattice‐based blind signature algorithm (L_BSA), which is a combination of lattice cryptography and a blind signature algorithm. From the generated random keys, the most optimal key is then selected by the Puzzle Optimization Algorithm (POA), which is then made available to the encryption phase. Then, the upgraded Merkle tree‐assisted vacuum filter (Vac‐UMT) algorithm is executed to accomplish the encryption task. Then the data are converted into blocks using blockchain technology and uploaded to the cloud. When receiving the audit requests, the verification process is carried out, and the evidence report is generated for the users. The proposed work is simulated in JAVA and assessed with the UNSW‐NB15 dataset, and the outcomes demonstrated that the system is highly efficient and secure. [ABSTRACT FROM AUTHOR]

Stopping power is the rate at which a material absorbs the kinetic energy of a charged particle passing through it--one of many properties needed over a wide range of thermodynamic conditions in modeling inertial fusion implosions. First-principles stopping calculations are classically challenging because they involve the dynamics of large electronic systems far from equilibrium, with accuracies that are particularly difficult to constrain and assess in the warm-dense conditions preceding ignition. Here, we describe a protocol for using a fault-tolerant quantum computer to calculate stopping power from a first-quantized representation of the electrons and projectile. Our approach builds upon the electronic structure block encodings of Su et al. [PRX Quant. 2, 040332 (2021)], adapting and optimizing those algorithms to estimate observables of interest from the non-Born-Oppenheimer dynamics of multiple particle species at finite temperature. We also work out the constant factors associated with an implementation of a high-order Trotter approach to simulating a grid representation of these systems. Ultimately, we report logical qubit requirements and leadingorder Toffoli costs for computing the stopping power of various projectile/target combinations relevant to interpreting and designing inertial fusion experiments. We estimate that scientifically interesting and classically intractable stopping power calculations can be quantum simulated with roughly the same number of logical qubits and about one hundred times more Toffoli gates than is required for state-of-the-art quantum simulations of industrially relevant molecules such as FeMoco or P450. [ABSTRACT FROM AUTHOR]

Quantum computing is a new discipline combining quantum mechanics and computer science, which is expected to solve technical problems that are difficult for classical computers to solve efficiently. At present, quantum algorithms and hardware continue to develop at a high speed, but due to the serious constraints of quantum devices, such as the limited numbers of qubits and circuit depth, the fault-tolerant quantum computing will not be available in the near future. Variational quantum algorithms(VQAs) using classical optimizers to train parameterized quantum circuits have emerged as the main strategy to address these constraints. However, VQAs still have many challenges, such as trainability, hardware noise, expressibility and entangling capability. The fundamental concepts and applications of VQAs are reviewed. Then, strategies are introduced to overcome the challenges of VQAs and the importance of further researching VQAs is highlighted. [ABSTRACT FROM AUTHOR]

Quantum computing has made many important achievements in the field of cryptanalysis. However, due to the limitations of current physical system and technology, the realization of large-scale universal quantum computers is a long way off. Currently, small-scale quantum computers are easier to implement than large-scale universal quantum computers. Distributed quantum computing proposes an implementation architecture, which attempts to break down large-scale tasks into many sub-tasks distributed across multiple small-scale quantum computers. How to use small-scale quantum computers with fewer qubits and shallower quantum depths to complete large-scale tasks and improve the success rate of attacking symmetric cryptosystems is our concern. In this paper, we propose a distributed exact Simon's algorithm, apply it to achieve quantum key recovery attacks on single-permutation-based pseudorandom cryptographic schemes with classical birthday bound security, and estimate the quantum resources of quantum circuits. Furthermore, we combine distributed exact Grover's algorithm and distributed exact Simon's algorithm to achieve quantum key recovery attacks on two-permutation-based pseudorandom cryptographic schemes with classical beyond birthday bound security and estimate the corresponding quantum resources. Our results show that (1) our algorithms are exact which means that the theoretical success probability of attacking pseudorandom cryptographic schemes is 100%; (2) the depth of circuit is in polynomial time which means that the theoretical depth of attacking symmetric cryptosystems is exponentially accelerated relative to the previous results; (3) the qubits of circuit don't increase significantly. Our work is of great importance. It could lead to the rapid realization of effective quantum attacks against symmetric cryptosystems on small-scale quantum computers. [ABSTRACT FROM AUTHOR]

This work introduces the use of a variational quantum circuit in order to perform unitary decomposition of a quantum operator. By use of classical optimization techniques and exploiting correlations and entanglement, the variational quantum circuit is able to translate a wide range of quantum algorithms, including the Toffoli gate and random unitary. A case study is also presented, where this decomposition is used to decompose a unitary matrix arise from a classification task. [ABSTRACT FROM AUTHOR]

Many existing static analysis algorithms suffer from cubic bottlenecks because of the need to compute a dynamic transitive closure (DTC). For the first time, this article studies the quantum speedups on searching subtasks in DTC-based static analysis algorithms using quantum search (e.g., Grover's algorithm). We first introduce our oracle implementation in Grover's algorithm for DTC-based static analysis and illustrate our quantum search subroutine. Then, we take two typical DTC-based analysis algorithms: context-free-language reachability and set constraint-based analysis, and show that our quantum approach can reduce the time complexity of these two algorithms to truly subcubic (\(O(N^2\sqrt {N}{\it polylog}(N))\)), yielding better results than the upper bound (O(N3/log N)) of existing classical algorithms. Finally, we conducted a classical simulation of Grover's search to validate our theoretical approach, due to the current quantum hardware limitation of lacking a practical, large-scale, noise-free quantum machine. We evaluated the correctness and efficiency of our approach using IBM Qiskit on nine open-source projects and randomly generated edge-labeled graphs/constraints. The results demonstrate the effectiveness of our approach and shed light on the promising direction of applying quantum algorithms to address the general challenges in static analysis. [ABSTRACT FROM AUTHOR]

In this paper, we explore the impact of quantum algorithms on classical network security. Our analysis focuses on Shor’s algorithm, which excels in factorizing large prime numbers, presenting a significant threat to classical cryptographic protocols. We conduct an in-depth analysis of Shor’s algorithm’s potential effects on HTTPS to highlight its disruptive capabilities. Moreover, to fortify classical cryptographic protocols against quantum threats, we introduce a novel Quantum Intrusion Prevention System (QIPS) scheme. Leveraging basic components like beam splitters and detectors, this solution serves as a dedicated hardware interface between the classical network and external quantum networks. Our proposed QIPS scheme offers enhanced resilience to classical cryptographic protocols, mitigating the vulnerabilities posed by quantum algorithms and reinforcing network security in the face of evolving threats. [ABSTRACT FROM AUTHOR]

In the past decade, quantum computing has undergone rapid evolution, capturing the increasing interest of the scientific community, industry, and governments. This enthusiasm has resulted in ambitious growth plans which stimulate the development of more efficient quantum computing devices and programming environments. The easy accessibility of quantum platforms in the cloud has attracted individuals to explore quantum computing, prompting a comprehensive analysis and assessment of quantum device's behavior. The extensive benchmarking presented in this study involved all free available quantum computing devices within the IBM Quantum Platform. These devices are employed to execute tens of thousands of quantum program executions, with the objective of evaluating quantum computer behavior and performance over time and under different optimization options. Special emphasis has been placed on analyzing the transpile operation and the depth of generated quantum circuits. The machine analysis tests are conducted using Quantum Computing Run Assistant (QCRA), a versatile software tool specifically designed to streamline the effortless distribution of quantum programs across a range of quantum computing platforms. This software not only streamlines the optimization of benchmarking processes but also simplifies the assessment of different configurations and result quality through the collection of advanced job metadata. [ABSTRACT FROM AUTHOR]

In this paper, we propose new Metropolis–Hastings and simulated annealing algorithms on a finite state space via modifying the energy landscape. The core idea of landscape modification rests on introducing a parameter c , such that the landscape is modified once the algorithm is above this threshold parameter to encourage exploration, while the original landscape is utilized when the algorithm is below the threshold for exploitation purposes. We illustrate the power and benefits of landscape modification by investigating its effect on the classical Curie–Weiss model with Glauber dynamics and external magnetic field in the subcritical regime. This leads to a landscape-modified mean-field equation, and with appropriate choice of c the free energy landscape can be transformed from a double-well into a single-well landscape, while the location of the global minimum is preserved on the modified landscape. Consequently, running algorithms on the modified landscape can improve the convergence to the ground state in the Curie–Weiss model. In the setting of simulated annealing, we demonstrate that landscape modification can yield improved or even subexponential mean tunnelling time between global minima in the low-temperature regime by appropriate choice of c , and we give a convergence guarantee using an improved logarithmic cooling schedule with reduced critical height. We also discuss connections between landscape modification and other acceleration techniques, such as Catoni's energy transformation algorithm, preconditioning, importance sampling, and quantum annealing. The technique developed in this paper is not limited to simulated annealing, but is broadly applicable to any difference-based discrete optimization algorithm by a change of landscape. [ABSTRACT FROM AUTHOR]

The foundation of this research is the quantum implementation of two hashing algorithms, namely Secure Hash Algorithm (SHA1) and Message Digest (MD5). Quantum cryptography is a challenging topic in network security for future networks. Quantum cryptography is an outgrowth of two broad topics—cryptology and cryptanalysis. In this paper, SHA1 and MD5 algorithms are designed and implemented for quantum computers. The main aim is to study and investigate the time requirement to build a hash and the bit rate at which a hash value is sent through. In this paper, a comprehensive analysis of these two algorithms is performed. Experiments have been done to compare and contrast the performances of the classical and proposed algorithms. In the experiment, it was found that the total time of execution of quantum SHA1 and quantum MD5 is much higher than the classical SHA1 and MD5. During quantum MD5 execution, it is observed that the time doubles when the number of chunks is increased from 1 to 2. Another experimental observation is that the execution time of the implemented algorithms depends upon the processor's speed. [ABSTRACT FROM AUTHOR]

Various iterative algorithms for solving the linear equation using a quantum computer operating on the principle of quantum annealing are studied. Assuming that the result produced by the computer is described by the Boltzmann distribution, conditions under which these algorithms converge are obtained and an estimate of their convergence rate is provided. Application of this approach for algorithms that use an infinite number of qubits and a small number of qubits is considered. [ABSTRACT FROM AUTHOR]

Pauli channels are fundamental in the context of quantum computing as they model the simplest kind of noise in quantum devices. We propose a quantum algorithm for simulating Pauli channels and extend it to encompass Pauli dynamical maps (parametrized Pauli channels). A parametrized quantum circuit is employed to accommodate for dynamical maps. We also establish the mathematical conditions for an N-qubit transformation to be achievable using a parametrized circuit where only one single-qubit operation depends on the parameter. The implementation of the proposed circuit is demonstrated using IBM's quantum computers for the case of one qubit, and the fidelity of this implementation is reported. [ABSTRACT FROM AUTHOR]

Recent years have seen significant advances in quantum/quantum-inspired technologies capable of approximately searching for the ground state of Ising spin Hamiltonians. The promise of leveraging such technologies to accelerate the solution of difficult optimization problems has spurred an increased interest in exploring methods to integrate Ising problems as part of their solution process, with existing approaches ranging from direct transcription to hybrid quantum- classical approaches rooted in existing optimization algorithms. While it is widely acknowledged that quantum computers should augment classical computers, rather than replace them entirely, comparatively little attention has been directed toward deriving analytical characterizations of their interactions. In this paper, we present a formal analysis of hybrid algorithms in the context of solving mixed-binary quadratic programs (MBQP) via Ising solvers. By leveraging an existing completely positive reformulation of MBQPs, as well as a new strong-duality result, we show the exactness of the dual problem over the cone of copositive matrices, thus allowing the resulting reformulation to inherit the straightforward analysis of convex optimization. We propose to solve this reformulation with a hybrid quantum-classical cutting-plane algorithm. Using existing complexity results for convex cutting-plane algorithms, we deduce that the classical portion of this hybrid framework is guaranteed to be polynomial time. This suggests that when applied to NP-hard problems, the complexity of the solution is shifted onto the subroutine handled by the Ising solver. [ABSTRACT FROM AUTHOR]

Quantum walks have proven to be a universal model for quantum computation and to provide speed-up in certain quantum algorithms. The discrete-time quantum walk (DTQW) model, among others, is one of the most suitable candidates for circuit implementation due to its discrete nature. Current implementations, however, are usually characterized by quantum circuits of large size and depth, which leads to a higher computational cost and severely limits the number of time steps that can be reliably implemented on current quantum computers. In this work, we propose an efficient and scalable quantum circuit implementing the DTQW on the 2 n -cycle based on the diagonalization of the conditional shift operator. For t time steps of the DTQW, the proposed circuit requires only O (n 2 + n t) two-qubit gates compared to the O (n 2 t) of the current most efficient implementation based on quantum Fourier transforms. We test the proposed circuit on an IBM quantum device for a Hadamard DTQW on the 4-cycle and 8-cycle characterized by periodic dynamics and by recurrent generation of maximally entangled single-particle states. Experimental results are meaningful well beyond the regime of few time steps, paving the way for reliable implementation and use on quantum computers. [ABSTRACT FROM AUTHOR]

With the recent advances in experimental realization of multi-qubit systems the idea of delegating certain real-life optimization tasks to a quantum computer becomes viable. In particular, we herein examine a variational quantum algorithm applied to a three-dimensional problem of open-pit mining, where the core of the classical optimization loop is provided by the probabilistic tensor sampling method. The developed technique is challenged against conventional optimization routines subjected to the essential optimization issues in variational quantum algorithms such as barren plateaus and multiple local minima. We demonstrate that the probabilistic tensor train-based approach allows one to steadily identify the ground state of a given system. [ABSTRACT FROM AUTHOR]

Quantum multidimensional scaling is a quantum dimensionality reduction algorithm. Its complex quantum circuit design structure and excessive qubits consumption make it difficult to run on the current quantum computers. In order to solve this problem, this paper proposes the variational quantum multidimensional scaling algorithm based on the variational quantum algorithm. Utilizing the parallel advantages of quantum computing to quickly compute low-dimensional embeddings of high-dimensional data, the variational quantum multidimensional scaling algorithm can provide lower time complexity; compared with the non-variational quantum multidimensional scaling algorithm, the variational quantum multidimensional scaling algorithm provides a simpler quantum circuit. In the noisy intermediate scale quantum era, the algorithm can run on a quantum computer. In addition, the article finally implemented the variational quantum multidimensional scaling algorithm on the Qiskit framework, proving the correctness of the algorithm. [ABSTRACT FROM AUTHOR]

The rapid development of quantum computing has led to increasing interest in quantum algorithms for a variety of different applications. Quantum walks have also experienced a surge in interest due to their potential use in quantum algorithms. Using the qiskit software package, we test how accurately the current generation of quantum computers provided by IBM can simulate a cycle discrete-time quantum walk. Implementing an 8-node, 8-step walk and a simpler 4-node, 4-step discrete-time quantum walk on an IBM quantum device known as ibmq_quito, the results for each step of the respective walks are presented. A custom noise model is developed in order to estimate that noise levels in the ibmq_santiago quantum device would need to be reduced by at least 94% in order to execute a 16-node, 16-step cycle discrete-time quantum walk to a reasonable level of fidelity. [ABSTRACT FROM AUTHOR]

With the rapid development of information technology, the amount of information in all walks of life has also increased sharply, and the information that people face is heterogeneous, large-scale and dynamic. This is an urgent problem to be solved in the research of data mining system based on heterogeneous cellular network algorithm, and it is also the focus of academic attention. At present, entrepreneurship has become an important way for college students to find employment. However, the risks and challenges of entrepreneurship are also increasing, so it is necessary to find an innovative way to solve these problems. This paper aims to explore the application of quantum computing based on heterogeneous cellular network algorithm in college students' entrepreneurial management, in order to provide a new solution. This paper studies the basic principle of heterogeneous cellular network algorithm and quantum computing, and puts forward the method of applying these two technologies to college students' entrepreneurial management. By using heterogeneous cellular network algorithms to manage the flow of information during the startup process, and using quantum computing to optimize the decision-making process. After experiment and analysis, this method can improve the accuracy and efficiency of entrepreneurial decision-making, while reducing risks and challenges, with high feasibility and practicability, and can help college students better cope with the challenges in the process of entrepreneurship and achieve better results. [ABSTRACT FROM AUTHOR]

Variational quantum metrology represents a powerful tool to optimize estimation strategies, resulting particularly beneficial for multiparameter estimation problems that often suffer from limitations due to the curse of dimensionality and computational complexity. To overcome these challenges, we develop a variational approach able to efficiently optimize a quantum multiphase sensor. Leveraging the reconfigurability of an integrated photonic device, we implement a hybrid quantum-classical feedback loop able to enhance the estimation performances. The quantum circuit evaluations are used to compute the system partial derivatives by applying the parameter-shift rule, and thus reconstruct experimentally the Fisher information matrix. This in turn is adopted as the cost function of a classical learning algorithm run to optimize the measurement settings. Our experimental results showcase significant improvements in estimation accuracy and noise robustness, highlighting the potential of variational techniques for practical applications in quantum sensing and more generally in quantum information processing using photonic circuits. [ABSTRACT FROM AUTHOR]

The parameters of the quantum circuit in a variational quantum algorithm induce a landscape that contains the relevant information regarding its optimization hardness. In this work, we investigate such landscapes through the lens of information content, a measure of the variability between points in parameter space. Our major contribution connects the information content to the average norm of the gradient, for which we provide robust analytical bounds on its estimators. This result holds for any (classical or quantum) variational landscape. We validate the analytical understating by numerically studying the scaling of the gradient in an instance of the barren plateau problem. In such instance, we are able to estimate the scaling pre-factors in the gradient. Our work provides a way to analyze variational quantum algorithms in a data-driven fashion well-suited for near-term quantum computers. [ABSTRACT FROM AUTHOR]

This paper examines whether a quantum computer can efficiently simulate the time evolution of the Schrödinger particle in a one-dimensional infinite potential well. In order to solve the Schrödinger equation in the quantum register, an algorithm based on the Quantum Discrete Sine Transform (QDST) is applied. The paper compares the results obtained in this way with the results given by the previous method (based on the QFT algorithm). [ABSTRACT FROM AUTHOR]

Convolutional neural networks (CNNs) have proven to be a very efficient class of machine learning (ML) architectures for handling multidimensional data by maintaining data locality, especially in the field of computer vision. Data pooling, a major component of CNNs, plays a crucial role in extracting important features of the input data and downsampling its dimensionality. Multidimensional pooling, however, is not efficiently implemented in existing ML algorithms. In particular, quantum machine learning (QML) algorithms have a tendency to ignore data locality for higher dimensions by representing/flattening multidimensional data as simple one-dimensional data. In this work, we propose using the quantum Haar transform (QHT) and quantum partial measurement for performing generalized pooling operations on multidimensional data. We present the corresponding decoherence-optimized quantum circuits for the proposed techniques along with their theoretical circuit depth analysis. Our experimental work was conducted using multidimensional data, ranging from 1-D audio data to 2-D image data to 3-D hyperspectral data, to demonstrate the scalability of the proposed methods. In our experiments, we utilized both noisy and noise-free quantum simulations on a state-of-the-art quantum simulator from IBM Quantum. We also show the efficiency of our proposed techniques for multidimensional data by reporting the fidelity of results. [ABSTRACT FROM AUTHOR]

This paper presents a system for solving binary-valued linear equations using quantum computers. The system is called Mod2VQLS, which stands for Modulo 2 Variational Quantum Linear Solver. As far as we know, this is the first such proposal. The design is a classical–quantum hybrid. The quantum components are a new circuit design for implementing matrix multiplication modulo 2, and a variational circuit to be optimized. The classical components are the optimizer, which measures the cost function and updates the quantum parameters for each iteration, and the controller that runs the quantum job and classical optimizer iterations. We propose two alternative ansatze or templates for the variational circuit and present results showing that the rotation ansatz designed specifically for this problem provides the most direct path to a valid solution. Numerical experiments in low dimensions indicate that Mod2VQLS, using the custom rotations ansatz, is on par with the block Wiedemann algorithm, which is the best-known to date solution for this problem. [ABSTRACT FROM AUTHOR]

Authentication in the digital landscape faces persistent challenges due to evolving cyber threats. Traditional text-based passwords, which are vulnerable to various attacks, necessitate innovative solutions to fortify user systems. This paper introduces the RoseCliff Algorithm, which is a dual authentication mechanism designed to enhance resilience against sophisticated hacking attempts and to continuously evolve stored passwords. The study explores encryption techniques, including symmetric, asymmetric, and hybrid encryption, thereby addressing the emerging threats posed by quantum computers. The RoseCliff Algorithm introduces introduces dynamism into passwords that allows for more secured communication across multiple platforms. To assess the algorithm's robustness, potential attacks such as brute force, dictionary attacks, man-in-the-middle attacks, and machine learning-based attacks are examined. The RoseCliff Algorithm, through its dynamic password generation and encryption methodology, proves effective against these threats. Usability evaluation encompasses the implementation and management phase, focusing on seamless integration, and the user experience, emphasizing clarity and satisfaction. Limitations are acknowledged, thus urging further research into encryption technique resilience, robustness against breaches, and the integration of emerging technologies. In conclusion, the RoseCliff Algorithm emerges as a promising solution, thereby effectively addressing the complexities of modern authentication challenges and providing a foundation for future research and enhancements in digital security. [ABSTRACT FROM AUTHOR]

Quantum approximate optimization algorithm (QAOA) is a promising hybrid quantum-classical algorithm to solve combinatorial optimization problems in the era of noisy intermediate-scale quantum computers. Recently it has been revealed that warm-start approaches can improve the performance of QAOA, where approximate solutions are obtained by classical algorithms in advance and incorporated into the initial state and/or unitary ansatz. In this work, we study in detail how the accuracy of approximate solutions affects the performance of the warm-start QAOA (WS-QAOA). We numerically find that in typical MAX-CUT problems, WS-QAOA achieves higher fidelity (probability that exact solutions are observed) and approximation ratio than QAOA as the Hamming distance of approximate solutions to the exact ones becomes smaller. We reveal that this could be quantitatively attributed to the initial state of the ansatz. We also solve MAX-CUT problems by WS-QAOA with approximate solutions obtained via QAOA, having higher fidelity and approximation ratio than QAOA especially when the circuit is relatively shallow. We believe that our study may deepen understanding of the performance of WS-QAOA and also provide a guide as to the necessary quality of approximate solutions. [ABSTRACT FROM AUTHOR]

Grover quantum algorithm is an unstructured search algorithm that can run on a quantum computer with the complexity of O N , and is one of the typical algorithms of quantum computing. Recently, it has served as a routine for pattern-matching tasks. However, the original Grover search algorithm is probabilistic, which is not negligible for problems involving determinism. Besides that, efficient data loading is also a key challenge for the practical applications of the Grover algorithm. Here in this work, we propose a modified pattern-matching scheme with Long's quantum search algorithm, in which the quantum circuit structure search algorithm requires fewer multi-qubit quantum gates, and can obtain the desired results deterministically. Then, the comparison of the performance of our scheme and the previous algorithms is presented through numerical simulations, indicating our algorithm is feasible with current quantum technologies which is friendly to noisy intermediate-scale quantum (NISQ) devices. [ABSTRACT FROM AUTHOR]

We investigate the possibility to calculate the ground‐state energy of the atomic systems on a quantum computer. For this purpose we evaluate the lowest binding energy of the moscovium atom with the use of the iterative phase estimation and variational quantum eigensolver (VQE). The calculations by the VQE are performed with a disentangled unitary coupled cluster ansatz and with various types of hardware‐efficient ansatze. The optimization is performed with the use of the Adam and quantum natural gradients procedures. The scalability of the ansatze and optimizers is tested by increasing the size of the basis set and the number of active electrons. The number of gates required for the iterative phase estimation and VQE is also estimated. [ABSTRACT FROM AUTHOR]

Quantum computers have been proposed to solve a number of important problems such as discovering new drugs, new catalysts for fertilizer production, breaking encryption protocols, optimizing financial portfolios, or implementing new artificial intelligence applications. Yet, to date, a simple task such as multiplying 3 by 5 is beyond existing quantum hardware. This article examines the difficulties that would need to be solved for quantum computers to live up to their promises. I discuss the whole stack of technologies that has been envisioned to build a quantum computer from the top layers (the actual algorithms and associated applications) down to the very bottom ones (the quantum hardware, its control electronics, cryogeny, etc.) while not forgetting the crucial intermediate layer of quantum error correction. [ABSTRACT FROM AUTHOR]

Since the mention of the Fourth Industrial Revolution in 2016, quantum computers and quantum computing (QC) have emerged as key technologies. Many researchers are trying to realize quantum computers and quantum computing. In particular, most of the development and application of metaheuristics algorithms using quantum computing is focused on computer engineering fields. Cases in which the developed algorithm is applied to the optimal design of a building or the optimal design results presented by expanding the algorithm in various directions are very insufficient. Therefore, in this paper, we proposed four methods of adopting qubits to perform pitch adjusting in the optimization process of the QbHS (quantum-based harmony search) algorithm and applied it to TTO (truss topology optimization) using four methods to compare the results. The four methods of adopting qubits have the same or decreased number of qubits adopted as the number of iterations changes. As a result of applying TTO using four methods, convergence performance differed depending on the adoption method, and convergence performance was superior to conventional HS (harmony search) algorithms in all methods. The optimal design of structural engineering using such QC is expected to contribute to the revitalization of future technologies in the architectural field and the field of computer information systems. [ABSTRACT FROM AUTHOR]

In recent years, quantum algorithms have emerged as a groundbreaking approach toward solving complex computational problems, particularly in physical modeling and artificial intelligence. This study introduces a novel quantum algorithm termed the duality game, tailored for addressing challenges in body dynamics modeling. The practicality and efficacy of the proposed algorithm are elucidated through three distinct data scenarios: (1) approximation of classical von Bertalanffy growth in the presence of random noise (simulated), (2) personalized tumor burden modeling leveraging a small dataset, and (3) modeling of COVID-19 population growth employing big data analytics. The algorithm's performance in these scenarios underscores its potential for practical applications at a large scale. Moreover, the findings foster optimism regarding the algorithm's promise in the burgeoning field of physical-based quantum artificial intelligence (quantum AI). Through the duality game, a pathway is delineated for addressing real-world problems in body dynamics, opening avenues for further research and development in quantum AI, aimed at harnessing quantum computational advantages for solving intricate physical modeling problems. [ABSTRACT FROM AUTHOR]

The development of mobile technologies and their integration with Internet of Things and smart technologies form both cyber-physical and socio-cyber-physical systems. In such systems, as a rule, wireless communication channels are used, in which SSL/TLS protocols are used to provide security services (confidentiality, integrity and authenticity). However, this protocol is not only vulnerable to "Meeting in the Middle", POODLE, BEAST, CRIME, BREACH attacks, but with the advent of a full-scale quantum computer, it can be broken. The article proposes a protocol based on quantum algorithms – crypto-code constructions, 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 McEliece and Niederreiter crypto-code constructions and the improved UMAC algorithm based on McEliece crypto-code design. The use of crypto-code constructions provides not only resistance to attacks, but also simplifies the formation of a connection – the parameters of elliptic curves are used for the transmission of the common key. This approach significantly reduces the time of connecting mobile gadgets and simplifies the procedure of agreement before data transfer. [ABSTRACT FROM AUTHOR]

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Mixed quantum-classical dynamics is a set of methods often used to understand systems too complex to treat fully quantum mechanically. Many techniques exist for full quantum mechanical evolution on quantum computers, but mixed quantum-classical dynamics are less explored. We present a modular algorithm for general mixed quantum-classical dynamics where the quantum subsystem is coupled with the classical subsystem. We test it on a modified Shin-Metiu model in the first quantization through Ehrenfest propagation. We find that the Time-Dependent Variational Time Propagation algorithm performs well for short-time evolutions and retains qualitative results for longer-time evolutions. The full-quantum propagation of molecular degrees of freedom is onerous even for the capability of noisy intermediate-scale quantum devices (NISQ), and methods to perform mixed quantum-classical dynamics on NISQ devices are at an early stage of development. The authors present a modular algorithm to perform mixed quantum-classical dynamics NISQ devices. [ABSTRACT FROM AUTHOR]

The elliptic curve discrete logarithm problem (ECDLP) is a popular choice for cryptosystems due to its high level of security. However, with the advent of the extended Shor's algorithm, there is concern that ECDLP may soon be vulnerable. While the algorithm does offer hope in solving ECDLP, it is still uncertain whether it can pose a real threat in practice. From the perspective of the quantum circuits of the algorithm, this paper analyzes the feasibility of cracking ECDLP using an ion trap quantum computer with improved quantum circuits for the extended Shor's algorithm. We give precise quantum circuits for extended Shor's algorithm to calculate discrete logarithms on elliptic curves over prime fields, including modular subtraction, three different modular multiplication, and modular inverse. Additionally, we incorporate and improve upon windowed arithmetic in the circuits to reduce the CNOT-counts. Whereas previous studies mostly focused on minimizing the number of qubits or the depth of the circuit, we focus on minimizing the number of CNOT gates in the circuit, which greatly affects the running time of the algorithm on an ion trap quantum computer. Specifically, we begin by presenting implementations of basic arithmetic operations with the lowest known CNOT-counts, along with improved constructions for modular inverse, point addition, and windowed arithmetic. Next, we precisely estimate that, to execute the extended Shor's algorithm with the improved circuits to factor an n-bit integer, the CNOT-count required is 1237 n 3 / log n + 2 n 2 + n . Finally, we analyze the running time and feasibility of the extended Shor's algorithm on an ion trap quantum computer. [ABSTRACT FROM AUTHOR]

In the field of data processing and IoT communication it is possible to develop more robust solutions by combining quantum algorithms with metaheuristics. Said solutions can be applied in the industry and be measured using metrics associated with complexity, efficiency, processing, and accuracy. An extensive bibliographical review is carried out to determine which is the most efficient and effective hybrid algorithm that can be applied to a real experimental case, which aims to improve communication to reduce occupational risks. Criteria, metrics, and experimental results were obtained, in which it is shown that the quantum genetic algorithm is better than the genetic algorithm. A detailed discussion on the objective function, the convergence to the global optimum, and the need to improve the obtained solutions is given. The conclusions raise new aspects that need investigation. [ABSTRACT FROM AUTHOR]

Since the RSA public key cryptosystem was proposed, it has been widely used because of its strong security. Although the proposal of the Shor's algorithm offers hope for cracking RSA, it is debatable whether the algorithm can actually pose a threat in practice. From the perspective of the quantum circuit of the Shor's algorithm, we analyse the feasibility of cracking RSA with improved quantum circuits using an ion-trap quantum computer. We present an improved quantum circuit for the modular exponentiation of a constant, which is the most expensive operation in Shor's algorithm for integer factorization. Whereas previous studies mostly focused on minimizing the number of qubits or the depth of the circuit, we minimize the number of CNOTs, which greatly affects the time to run the algorithm on an ion-trap quantum computer. First, we give the implementation of the basic arithmetic with the lowest known number of CNOTs and the construction of an improved modular exponentiation of a constant by accumulating intermediate data and using a windowing technique. Then, we precisely estimate the number of improved quantum circuits needed to perform the Shor's algorithm for factoring an n -bit integer, which is 217 n 3 / log 2 n + 4 n 2 + n. We analyse the running time and feasibility of the Shor's algorithm on an ion-trap quantum computer according to the number of CNOTs. Finally, we discussed the lower bound of the number of CNOTs needed to implement the Shor's algorithm. [ABSTRACT FROM AUTHOR]

Most of current public key cryptosystems would be vulnerable to the attacks of the future quantum computers. Post-quantum cryptography offers mathematical methods to secure information and communications against such attacks, and therefore has been receiving a significant amount of attention in recent years. Lattice-based cryptography, built on the mathematical hard problems in (high-dimensional) lattice theory, is a promising post-quantum cryptography family due to its excellent efficiency, moderate size and strong security. This survey aims to give a general overview on lattice-based cryptography. To this end, the authors begin with the introduction of the underlying mathematical lattice problems. Then they introduce the fundamental cryptanalytic algorithms and the design theory of lattice-based cryptography. [ABSTRACT FROM AUTHOR]