Quantum walks (QWs) have a property that classical random walks (RWs) do not possess—the coexistence of linear spreading and localization—and this property is utilized to implement various kinds of applications. This paper proposes RW- an...
We propose a model that interpolates between quantum walks and persistent (correlated) random walks using one parameter on the one-dimensional lattice. We show that the limit distribution is described by the normal variance mixture with the arcsine law.
In intercity expressway traffic, the multiplicity of available routes leads to randomness in exit selection. Random exit selection by drivers is hard to observe, and thus it is a challenge to model intercity expressway traffic sufficiently. In this p...
The analysis of the return probability is one of the most essential and fundamental topics in the study of classical random walks. In this paper, we study the return probability of quantum and correlated random walks in the one-dimensional integer la...
Quantum Markov chains (QMCs) and open quantum random walks (OQRWs) represent different quantum extensions of the classical Markov chain framework. QMCs stand as a more profound layer within the realm of Markovian dynamics. The exploration of both QMC...
This paper proposes an encryption scheme for high pixel density images. Based on the application of the quantum random walk algorithm, the long short-term memory (LSTM) can effectively solve the problem of low efficiency of the quantum random walk al...
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...
For many years, chaotic maps have been widely used in the design of various algorithms in cryptographic systems. In this paper, a new model (compound chaotic system) of quantum random walks controlled by a hyper-chaotic map is constructed and a novel...
Protein–protein interaction (PPI) networks consist of the physical and/or functional interactions between the proteins of an organism, and they form the basis for the field of network medicine. Since the biophysical and high-throughput methods...
In this work, the quantum random walk search algorithm with a walk coin constructed by generalized Householder reflection and phase multiplier has been studied. The coin register is one qudit with an arbitrary dimension. Monte Carlo simulations, in c...
Markov processes, such as random walk models, have been successfully used by cognitive and neural scientists to model human choice behavior and decision time for over 50 years. Recently, quantum walk models have been introduced as an alternative way...
Many hacking incidents are linked to work files because most companies work with them. However, a variety of file encryption and decryption methods have been proposed. Existing file encryption/decryption technologies are under threat as hacking techn...
In the framework of an exactly soluble model, one considers a typical problem of the interaction between radiation and matter: the dynamics of population in a multilevel quantum system subject to a time dependent perturbation. The algebraic structure...
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 ch...
In this paper, a surjective mapping that satisfies the Li–Yorke chaos in the unit area is constructed and a perturbation algorithm (disturbing its parameters and inputs through another high-dimensional chaos) is proposed to enhance the randomne...
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 p...
Maze-solving by natural phenomena is a symbolic result of the autonomous optimization induced by a natural system. We present a method for finding the shortest path on a maze consisting of a bipartite graph using a discrete-time quantum walk, which i...
We consider quantum extensions of classical hydrodynamic lattice gas models. We find that the existence of local conserved quantities strongly constrains such extensions. We find the only extensions that retain local conserved quantities correspond t...
In this paper, we consider the time averaged distribution of discrete time quantum walks on the glued trees. In order to analyze the walks on the glued trees, we consider a reduction to the walks on path graphs. Using a spectral analysis of the Jacob...
The purpose of this article is to highlight the connections between two seemingly distinct domains: random walks and the distribution of angular-momentum projections in quantum physics (the magnetic quantum numbers m). It is well known that there is...
The quantum proxy signature is one of the most significant formalisms in quantum signatures. We put forward a quantum proxy signature scheme using quantum walk-based teleportation and quantum one-time pad CNOT (QOTP-CNOT) operation, which includes fo...
We study discrete-time quantum walks on generalized Birkhoff polytope graphs (GBPGs), which arise in the solution-set to certain transportation linear programming problems (TLPs). It is known that quantum walks mix at most quadratically faster than r...
We claim that quantum collapse, as per the Copenhagen interpretation of quantum mechanics, follows naturally from the energetics of measurement. We argue that a realistic device generates an interaction energy that drives a random walk in Hilbert spa...
We present the single-particle sector of a quantum cellular automaton, namely a quantum walk, on a simple dynamical triangulated
Combs are a simple caricature of various types of natural branched structures, which belong to the category of loopless graphs and consist of a backbone and branches. We study two generalizations of comb models and present a generic method to obtain...
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_mat...
We describe particles in a potential by a special diffusion process, the maximal entropy random walk (MERW) on a lattice. Since MERW originates in a variational problem, it shares the linear algebra of Hilbert spaces with quantum mechanics. The Born...
This exploratory study investigates a human agent’s evolving judgements of reliability when interacting with an AI system. Two aims drove this investigation: (1) compare the predictive performance of quantum vs. Markov random walk models regard...
The non-Markovianity of open quantum system dynamics is often associated with the bidirectional interchange of information between the system and its environment, and it is thought to be a resource for various quantum information tasks. We have inves...
We have implemented quantum modeling mainly based on Bohmian mechanics to study time series that contain strong coupling between their events. Compared to time series with normal densities, such time series are associated with rare events. Hence, emp...
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-s...
Incorporating insights from quantum theory, we propose a machine learning-based decision-making model, including a logic tree and a value tree; a genetic programming algorithm is applied to optimize both the logic tree and value tree. The logic tree...
A classical random walker starting on a node of a finite graph will always reach any other node since the search is ergodic, namely it fully explores space, hence the arrival probability is unity. For quantum walks, destructive interference may induc...
Since the dynamical behavior of chaotic and stochastic systems is very similar, it is sometimes difficult to determine the nature of the movement. One of the best-studied stochastic processes is Brownian motion, a random walk that accurately describe...
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 corresponde...
Improving the Bose–Einstein condensate model of dark matter through the repulsive three-particle interaction to better reproduce observables such as rotation curves reveals both different thermodynamic phases and few-particle correlations. Usin...
Quantum sensors are expected to offer significant advantages in magnetic- and gravity-aided navigation. However, these techniques depend on the local environmental conditions and require an alternative solution to ensure high position accuracy on sho...
Organic disordered semiconductors have a growing importance because of their low cost, mechanical flexibility, and multiple applications in thermoelectric devices, biosensors, and optoelectronic devices. Carrier transport consists of variable-range h...
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...
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 m...