Search Results (104)

The Learning with Errors (LWE) problem, particularly its efficient ternary variant where secrets and errors are small, is a fundamental building block for numerous post-quantum cryptographic schemes. Combinatorial attacks provide a potent approach to cryptanalyzing ternary LWE. While classical attacks have achieved complexities close to their asymptotic ${\mathcal{S}}^{0.25}$ bound for a search space of size $\mathcal{S}$, their quantum counterparts have faced a significant gap: the attack by van Hoof et al. (vHKM) only reached a concrete complexity of ${\mathcal{S}}^{0.251}$, far from its asymptotic promise of ${\mathcal{S}}^{0.193}$. This work introduces an efficient quantum combinatorial attack that substantially narrows this gap. We present a quantum walk adaptation of the locality-sensitive hashing algorithm by Kirshanova and May, which fundamentally removes the need for guessing error coordinates—the primary source of inefficiency in the vHKM approach. This crucial improvement allows our attack to achieve a concrete complexity of approximately ${\mathcal{S}}^{0.225}$, markedly improving over prior quantum combinatorial methods. For concrete parameters of major schemes including NTRU, BLISS, and GLP, our method demonstrates substantial runtime improvements over the vHKM attack, achieving speedup factors ranging from $2^{16}$ to $2^{60}$ across different parameter sets and establishing the new state-of-the-art for quantum combinatorial attacks. As a second contribution, we address the challenge of polynomial quantum memory constraints. We develop a hybrid approach combining the Kirshanova–May framework with a quantum claw-finding technique, requiring only $\mathcal{O}\left(n\right)$ qubits while utilizing exponential classical memory. This work provides the first comprehensive concrete security analysis of real-world LWE-based schemes under such practical quantum resource constraints, offering crucial insights for post-quantum security assessments. Our results reveal a nuanced landscape where our combinatorial attacks are superior for small-weight parameters, while lattice-based attacks maintain an advantage for others. Full article

We evaluate a hybrid quantum–classical pipeline for speech emotion recognition (SER) on a custom Afrikaans corpus using MFCC-based spectral features with pitch and energy variants, explicitly comparing three quantum approaches—a variational quantum classifier (VQC), a quantum support vector machine (QSVM), and a Quantum Approximate Optimisation Algorithm (QAOA)-based classifier—against a CNN–LSTM (CLSTM) baseline. We detail the classical-to-quantum data encoding (angle embedding with bounded rotations and an explicit feature-to-qubit map) and report test accuracy, weighted precision, recall, and F1. Under ideal analytic simulation, the quantum models reach 41–43% test accuracy; under a realistic 1% NISQ noise model (100–1000 shots) this degrades to 34–40%, versus 73.9% for the CLSTM baseline. Despite the markedly lower empirical accuracy—expected in the NISQ era—we provide an end-to-end, noise-aware hybrid SER benchmark and discuss the asymptotic advantages of quantum subroutines (Chebyshev-based quantum singular value transformation, quantum walks, and block encoding) that become relevant only in the fault-tolerant regime. Full article

The subset-sum problem, a foundational NP-hard problem in theoretical computer science, serves as a critical building block for cryptographic constructions. This work introduces novel classical and quantum heuristic algorithms for the random subset-sum problem at density $d=1$, where exactly one solution is expected. Classically, we propose the first algorithm based on a ternary tree representation structure, inspired by recent advances in lattice-based cryptanalysis. Through numerical optimization, our method achieves a time complexity of $\widetilde{𝒪}\left(2^{0.2400n}\right)$ and space complexity of $\widetilde{𝒪}\left(2^{0.2221n}\right)$, improving upon the previous best classical heuristic result of $\widetilde{𝒪}\left(2^{0.2830n}\right)$. In the quantum setting, we develop a corresponding algorithm by integrating the classical ternary representation technique with a quantum walk search framework. The optimized quantum algorithm attains a time and space complexity of $\widetilde{𝒪}\left(2^{0.1843n}\right)$, surpassing the prior state-of-the-art quantum heuristic of $\widetilde{𝒪}\left(2^{0.2182n}\right)$. Furthermore, we apply our algorithms to information set decoding in code-based cryptography. For half-distance decoding, our classical algorithm improves the time complexity to $\widetilde{𝒪}\left(2^{0.0453n}\right)$, surpassing the previous best of $\widetilde{𝒪}\left(2^{0.0465n}\right)$. For full-distance decoding, we achieve a quantum complexity of $\widetilde{𝒪}\left(2^{0.058326n}\right)$, advancing beyond the prior best quantum result of $\widetilde{𝒪}\left(2^{0.058696n}\right)$. These findings demonstrate the broad applicability and efficiency of our ternary representation technique across both classical and quantum computational models. Full article

Quantum walks are, at present, an active field of study in mathematics, with important applications in quantum information and statistical physics. In this paper, we determine the influence of basic chaotic features on the walker behavior. For this purpose, we consider an extremely simple model consisting of alternating one-dimensional walks along the two spatial coordinates in bidimensional closed domains (hard wall billiards). The chaotic or regular behavior induced by the boundary shape in the deterministic classical motion translates into chaotic signatures for the quantized problem, resulting in sharp differences in the spectral statistics and morphology of the eigenfunctions of the quantum walker. Indeed, we found, for the Bunimovich stadium—a chaotic billiard—level statistics described by a Brody distribution with parameter $\delta \simeq 0.1$. This indicates a weak level repulsion, and also enhanced eigenfunction localization, with an average participation ratio $(\mathrm{PR})\simeq 1150$ compared to the rectangular billiard (regular) case, where the average $\mathrm{PR}\simeq 1500$. Furthermore, scarring on unstable periodic orbits is observed. The fact that our simple model exhibits such key signatures of quantum chaos, e.g., non-Poissonian level statistics and scarring, that are sensitive to the underlying classical dynamics in the free particle billiard system is utterly surprising, especially when taking into account that quantum walks are diffusive models, which are not direct quantizations of a Hamiltonian. Full article

Creative insight is a core phenomenon of human cognition, often characterized by the sudden emergence of novel and contextually appropriate ideas. Classical models based on symbolic search or associative networks struggle to capture the non-linear, context-sensitive, and interference-driven aspects of insight. In this work, we propose a computational model of insight generation grounded in continuous-time quantum walks over weighted semantic graphs, where nodes represent conceptual units and edges encode associative relationships. By exploiting the principles of quantum superposition and interference, the model enables the probabilistic amplification of semantically distant but contextually relevant concepts, providing a plausible account of non-local transitions in thought. The model is implemented using standard Python 3.10 libraries and is available both as an interactive fully reproducible Google Colab notebook and a public repository with code and derived datasets. Comparative experiments on ConceptNet-derived subgraphs, including the Candle Problem, 20 Remote Associates Test triads, and Alternative Uses, show that, relative to classical diffusion, quantum walks concentrate more probability on correct targets (higher AUC and peaks reached earlier) and, in open-ended settings, explore more broadly and deeply (higher entropy and coverage, larger expected radius, and faster access to distant regions). These findings are robust under normalized generators and a common time normalization, align with our formal conditions for transient interference-driven amplification, and support quantum-like dynamics as a principled process model for key features of insight. Full article

The basic Salp Swarm Algorithm (SSA) offers advantages such as a simple structure and few parameters. However, it is prone to falling into local optima and remains inadequate for seed classification tasks that involve hyperparameter optimization of machine learning classifiers such as Support Vector Machines (SVMs). To overcome these limitations, an Enhanced Knowledge-based Salp Swarm Algorithm (EKSSA) is proposed. The EKSSA incorporates three key strategies: Adaptive adjustment mechanisms for parameters $c_1$ and $\alpha$ to better balance exploration and exploitation within the salp population; a Gaussian walk-based position update strategy after the initial update phase, enhancing the global search ability of individuals; and a dynamic mirror learning strategy that expands the search domain through solution mirroring, thereby strengthening local search capability. The proposed algorithm was evaluated on thirty-two CEC benchmark functions, where it demonstrated superior performance compared to eight state-of-the-art algorithms, including Randomized Particle Swarm Optimizer (RPSO), Grey Wolf Optimizer (GWO), Archimedes Optimization Algorithm (AOA), Hybrid Particle Swarm Butterfly Algorithm (HPSBA), Aquila Optimizer (AO), Honey Badger Algorithm (HBA), Salp Swarm Algorithm (SSA), and Sine–Cosine Quantum Salp Swarm Algorithm (SCQSSA). Furthermore, an EKSSA-SVM hybrid classifier was developed for seed classification, achieving higher classification accuracy. Full article

Quantum computers are emerging as a major tool in the computation field, leveraging the principles of quantum mechanics to solve specific problems currently beyond the capability of classical computers. This technology holds significant promise in edge-main cloud deployments, where it can enable low-latency data processing and secure communication. This paper aims to establish a research foundation by integrating quantum computing with classical edge-cloud environments to promote performance across a range of applications that scientists are actively investigating. However, the successful deployment of hybrid quantum–classical edge-clouds requires a comprehensive evaluation framework to ensure their alignment with the performance requirements. This study first proposes a novel quantum benchmarking framework, including two distinct methods to evaluate latency scores based on the quantum transpilation levels across different quantum-edge-cloud platforms. The framework is then validated for the edge-cloud environment by benchmarking several well-known and useful quantum algorithms potentially useful in this domain, including Shor’s, Grover’s, and the Quantum Walks algorithm. An optimal transpilation level is eventually suggested to achieve maximum performance in quantum-edge-cloud environments. In summary, this research paper provides critical insights into the current and prospective capabilities of QPU integration, offering a novel benchmarking framework and providing a comprehensive assessment of their potential to enhance edge-cloud performance under varying parameters, including fidelity and transpilation levels. Full article

This paper presents a novel approach to enhancing the security of error correction in quantum key distribution by introducing randomization into the update rule of Tree Parity Machines. Two dynamic update algorithms—dynamic_rows and dynamic_matrix—are proposed and tested. These algorithms select the update rule quasi-randomly based on the input vector, reducing the effectiveness of synchronization-based attacks. A series of simulations were conducted to evaluate the security implications under various configurations, including different values of K, N, and L parameters of neural networks. The results demonstrate that the proposed dynamic algorithms can significantly reduce the attacker’s synchronization success rate without requiring additional communication overhead. Both proposed solutions outperformed hebbian, an update rule-based synchronization method utilizing the percentage of attackers synchronization. It has also been shown that when the attacker chooses their update rule randomly, the dynamic approaches work better compared to random walk rule-based synchronization, and that in most cases it is more profitable to use dynamic update rules when an attacker is using random walk. This study contributes to improving QKD’s robustness by introducing adaptive neural-based error correction mechanisms. Full article

Accurate wind-speed prediction plays an important role in improving the operation stability of wind-power generation systems. However, the inherent complexity of meteorological dynamics poses a major challenge to forecasting accuracy. In order to overcome these limitations, we propose a new hybrid framework, which combines variational mode decomposition (VMD) for signal processing, enhanced quantum particle swarm optimization (e-QPSO), an improved walking optimization algorithm (IHOA) for feature selection and the long short-term memory (LSTM) network, and which finally establishes a reliable prediction architecture. The purpose of this paper is to optimize VMD by using the e-QPSO algorithm to improve the problems of excessive filtering or error filtering caused by parameter problems in VMD, as the noise signal cannot be filtered completely, and the number of sources cannot be accurately estimated. The IHOA algorithm is used to find the optimal hyperparameters of LSTM to improve the learning efficiency of neurons and improve the fitting ability of the model. The proposed e-QPSO-VMD-IHOA-LSTM model is compared with six established benchmark models to verify its predictive ability. The effectiveness of the model is verified by experiments using the hourly wind-speed data measured in four seasons in Changchun in 2023. The MAPE values of the four datasets were 0.0460, 0.0212, 0.0263, and 0.0371, respectively. The results show that e-QPSO-VMD effectively processes the data and avoids the problem of error filtering, while IHOA effectively optimizes the LSTM parameters and improves prediction performance. Full article

Identifying influential nodes in complex networks is essential for a wide range of applications, from social network analysis to enhancing infrastructure resilience. While quantum walk-based methods offer potential advantages, existing approaches face challenges in dimensionality, computational efficiency, and accuracy. To address these limitations, this study proposes a novel method inspired by the one-dimensional discrete-time quantum walk (IOQW). This design enables the development of a simplified shift operator that leverages both self-loops and the network’s structural connectivity. Furthermore, degree centrality and path-based features are integrated into the coin operator, enhancing the accuracy and scalability of the IOQW framework. Comparative evaluations against state-of-the-art quantum and classical methods demonstrate that IOQW excels in capturing both local and global topological properties while maintaining a low computational complexity of $O(N⟨k⟩)$, where $⟨k⟩$ denotes the average degree. These advancements establish IOQW as a powerful and practical tool for influential node identification in complex networks, bridging quantum-inspired techniques with real-world network science applications. Full article

Topological transitions are relevant for boundary conditions. Therefore, we investigate the bulk spectra, edge states, and topological phases of Szegedy’s quantum search on a one-dimensional (1D) cycle with self-loops, where the search operator can be formulated as an open boundary condition. By establishing an equivalence with coined quantum walks (QWs), we analytically derive and numerically illustrate the quasienergies dispersion relations of bulk spectra and edge states for Szegedy’s quantum search. Interestingly, novel gapless three-band structures are observed, featuring a flat band and three-fold degenerate points. We identify the topological phases $\pm 2$ as the Chern number. This invariant is computed by leveraging chiral symmetry in zero diagonal Hermitian Hamiltonians that satisfy our quasienergies constraints. Furthermore, we demonstrate that the edge states enhance searches on the marked vertices, while the nontrivial bulk spectra facilitate ballistic spread for Szegedy’s quantum search. Crucially, we find that gapless topological phases arise from three-fold degenerate points and are protected by chiral symmetry, distinguishing ill-defined topological transition boundaries. Full article

We address the problem of routing quantum and classical information from one sender to many possible receivers in a network. By employing the formalism of quantum walks, we describe the dynamics on a discrete structure based on a complete graph, where the sites naturally provide a basis for encoding the quantum state to be transmitted. Upon tuning a single phase or weight in the Hamiltonian, we achieve near-unitary routing fidelity, enabling the selective delivery of information to designated receivers for both classical and quantum data. The structure is inherently scalable, accommodating an arbitrary number of receivers. The routing time is largely independent of the network’s dimension and input state, and the routing performance is robust under static and dynamic noise, at least for a short time. Full article

Recent work has demonstrated a correspondence that bridges quantum information processing and high-energy physics: discrete quantum cellular automata (QCA) can, in the continuum limit, reproduce quantum field theories (QFTs). This QCA/QFT correspondence raises fundamental questions about how matter/energy, information, and the nature of spacetime are related. Here, we show that free QED is equivalent to the continuous-space-and-time limit of Fermi and Bose QCA theories on the cubic lattice derived from quantum random walks satisfying simple symmetry and unitarity conditions. In doing so, we define the Fermi and Bose theories in a unified manner using the usual fermion internal space and a boson internal space that is six-dimensional. We show that the reduction to a two-dimensional boson internal space (two helicity states arising from spin-1 plus the photon transversality condition) comes from restricting the QCA theory to positive energies. We briefly examine common symmetries of QCAs and how time-reversal symmetry demands the existence of negative-energy solutions. These solutions produce a tension in coupling the Fermi and Bose theories, in which the strong locality of QCAs seems to require a non-zero amplitude to produce negative-energy states, leading to an unphysical cascade of negative-energy particles. However, we show in a 1D model that, by extending interactions over a larger (but finite) range, it is possible to exponentially suppress the production of negative-energy particles to the point where they can be neglected. Full article

Quantum walks are a powerful framework for simulating complex quantum systems and designing quantum algorithms, particularly for spatial search on graphs, where the goal is to find a marked vertex efficiently. In this work, we present efficient quantum circuits that implement the evolution operator of continuous-time quantum-walk-based search algorithms for three graph families: complete graphs, complete bipartite graphs, and hypercubes. For complete and complete bipartite graphs, our circuits exactly implement the evolution operator. For hypercubes, we propose an approximate implementation that closely matches the exact evolution operator as the number of vertices increases. Our Qiskit simulations demonstrate that even for low-dimensional hypercubes, the algorithm effectively identifies the marked vertex. Furthermore, the approximate implementation developed for hypercubes can be extended to a broad class of graphs, enabling efficient quantum search in scenarios where exact implementations are impractical. Full article