Search Results (97)

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

We investigate the quantum random walk in momentum space of a spinor kicked rotor with a non-Hermitian kicking potential. We find that the variance in momentum distributions transitions from quadratic to linear growth over time for the non-Hermitian case. Correspondingly, the momentum distributions are in the shape of Gaussian wavepackets, providing clear evidence of a classical random walk induced by the non-Hermitian-driven potential. Remarkably, the rate of the linear growth of the variance diverges as the non-Hermitian parameter approaches zero. In the Hermitian case, deviations from the quantum resonance condition dramatically suppress the quadratic growth of the variance, leading to dynamical localization of the quantum walk. Under such quantum non-resonance conditions, the classical random walk is significantly reduced by the non-Hermitian-driven potential. Interestingly, non-Hermiticity enhances quantum entanglement between internal degrees of freedom, while deviations from the quantum resonance condition reduce it. Possible applications of our findings are discussed. Full article

We start presenting an overview on recent applications of linear polymers and networks in condensed matter physics, chemistry and biology by briefly discussing selected papers (published within 2022–2024) in some detail. They are organized into three main subsections: polymers in physics (further subdivided into simulations of coarse-grained models and structural properties of materials), chemistry (quantum mechanical calculations, environmental issues and rheological properties of viscoelastic composites) and biology (macromolecules, proteins and biomedical applications). The core of the work is devoted to a review of theoretical aspects of linear polymers, with emphasis on self-avoiding walk (SAW) chains, in regular lattices and in both deterministic and random fractal structures. Values of critical exponents describing the structure of SAWs in different environments are updated whenever available. The case of random fractal structures is modeled by percolation clusters at criticality, and the issue of multifractality, which is typical of these complex systems, is illustrated. Applications of these models are suggested, and references to known results in the literature are provided. A detailed discussion of the reptation method and its many interesting applications are provided. The problem of protein folding and protein evolution are also considered, and the key issues and open questions are highlighted. We include an experimental section on polymers which introduces the most relevant aspects of linear polymers relevant to this work. The last two sections are dedicated to applications, one in materials science, such as fractal features of plasma-treated polymeric materials surfaces and the growth of polymer thin films, and a second one in biology, by considering among others long linear polymers, such as DNA, confined within a finite domain. Full article

We investigate a quantum walk on a ring represented by a directed triangle graph with complex edge weights and monitored at a constant rate until the quantum walker is detected. To this end, the first hitting time statistics are recorded using unitary dynamics interspersed stroboscopically by measurements, which are implemented on IBM quantum computers with a midcircuit readout option. Unlike classical hitting times, the statistical aspect of the problem depends on the way we construct the measured path, an effect that we quantify experimentally. First, we experimentally verify the theoretical prediction that the mean return time to a target state is quantized, with abrupt discontinuities found for specific sampling times and other control parameters, which has a well-known topological interpretation. Second, depending on the initial state, system parameters, and measurement protocol, the detection probability can be less than one or even zero, which is related to dark-state physics. Both return-time quantization and the appearance of the dark states are related to degeneracies in the eigenvalues of the unitary time evolution operator. We conclude that, for the IBM quantum computer under study, the first hitting times of monitored quantum walks are resilient to noise. However, a finite number of measurements leads to broadening effects, which modify the topological quantization and chiral effects of the asymptotic theory with an infinite number of measurements. Full article

In this work, the dynamics of a quantum walker on glued trees is revisited to understand the influence of the architecture of the graph on the efficiency of the transfer between the two roots. Instead of considering regular binary trees, we focus our attention on leafier structures where each parent node could give rise to a larger number of children. Through extensive numerical simulations, we uncover a significant dependence of the transfer on the underlying graph architecture, particularly influenced by the branching rate (M) relative to the root degree (N). Our study reveals that the behavior of the walker is isomorphic to that of a particle moving on a finite-size chain. This chain exhibits defects that originate in the specific nature of both the roots and the leaves. Therefore, the energy spectrum of the chain showcases rich features, which lead to diverse regimes for the quantum-state transfer. Notably, the formation of quasi-degenerate localized states due to significant disparities between M and N triggers a localization process on the roots. Through analytical development, we demonstrate that these states play a crucial role in facilitating almost perfect quantum beats between the roots, thereby enhancing the transfer efficiency. Our findings offer valuable insights into the mechanisms governing quantum-state transfer on trees, with potential applications for the transfer of quantum information. Full article

The double random phase encoding (DRPE) image encryption method has garnered significant attention in color image processing and optical encryption thanks to its R, G, and B parallel encryption. However, DRPE-based color image encryption faces two challenges. Firstly, it disregards the correlation of R, G, and B, compromising the encrypted image’s robustness. Secondly, DRPE schemes relying on Discrete Fourier Transform (DFT) and Discrete Fractional Fourier Transform (DFRFT) are vulnerable to linear attacks, such as Known Plaintext Attack (KPA) and Chosen Plaintext Attack (CPA). Quantum walk is a powerful tool for modern cryptography, offering robust resistance to classical and quantum attacks. Therefore, this study presents an optical color image encryption algorithm that combines two-dimensional quantum walking (TDQW) with 24-bit plane permutation, dubbed OCT. This approach employs pseudo-random numbers generated by TDQW for phase modulation in DRPE and scrambles the encrypted image’s real and imaginary parts using the generalized Arnold transform. The 24-bit plane permutation helps reduce the R, G, and B correlation, while the generalized Arnold transform bolsters DRPE’s resistance to linear attacks. By incorporating TDQW, the key space is significantly expanded. The experimental results validate the effectiveness and security of the proposed method. Full article

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 $O(n^2+nt)$ two-qubit gates compared to the $O\left(n^{2}t\right)$ 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. Full article

Phase transitions happen at critical values of the controlling parameters, such as the critical temperature in classical phase transitions, and system critical parameters in the quantum case. However, true criticality happens only at the thermodynamic limit, when the number of particles goes to infinity with constant density. To perform the calculations for the critical parameters, a finite-size scaling approach was developed to extrapolate information from a finite system to the thermodynamic limit. With the advancement in the experimental and theoretical work in the field of ultra-cold systems, particularly trapping and controlling single atomic and molecular systems, one can ask: do finite systems exhibit quantum phase transition? To address this question, finite-size scaling for finite systems was developed to calculate the quantum critical parameters. The recent observation of a quantum phase transition in a single trapped ¹⁷¹ Yb⁺ ion indicates the possibility of quantum phase transitions in finite systems. This perspective focuses on examining chemical processes at ultra-cold temperatures, as quantum phase transitions—particularly the formation and dissociation of chemical bonds—are the basic processes for understanding the whole of chemistry. Full article