Related papers: On the relation between quantum walks and zeta fun…
The purpose of this paper is to investigate coefficient matrices of functional equations of zeta functions associated with homogeneous cones, which are given explicitly in the previous paper, in detail. We prove that the coefficient matrix…
A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method [10]. This quantum model is then associated with a stochastic…
We apply a discrete quantum walk from a quantum particle on a discrete quantum spacetime from loop quantum gravity and show that the related Entanglement Entropy can drive a entropic force. We apply this concepts to propose a model of a…
We introduce a fidelity-based measure $\text{D}_{\text{CQ}}(t)$ to quantify the differences between the dynamics of classical (CW) and quantum (QW) walks over a graph. We provide universal, graph-independent, analytic expressions of this…
This paper presents a realistic, stochastic, and local model that reproduces nonrelativistic quantum mechanics (QM) results without using its mathematical formulation. The proposed model only uses integer-valued quantities and operations on…
Given the extensive application of classical random walks to classical algorithms in a variety of fields, their quantum analogue in quantum walks is expected to provide a fruitful source of quantum algorithms. So far, however, such…
We consider a spectral analysis on the quantum walks on graph $G=(V,E)$ with the local coin operators $\{C_u\}_{u\in V}$ and the flip flop shift. The quantum coin operators have commonly two distinct eigenvalues $\kappa,\kappa'$ and…
We study quantum transport on finite discrete structures and we model the process by means of continuous-time quantum walks. A direct and effective comparison between quantum and classical walks can be attained based on the average…
The foundational work of Karlin and McGregor established a powerful connection between random walks with tridiagonal transition matrices and the theory of orthogonal polynomials. We consider a particular extension of this framework, where…
We characterize the spectrum of the transition matrix for simple random walk on graphs consisting of a finite graph with a finite number of infinite Cayley trees attached. We show that there is a continuous spectrum identical to that for a…
This paper is motivated by the following problem. Define a quantum walk on a positively weighted path (linear chain). Can the weights be tuned so that perfect state transfer occurs between the first vertex and any other position? We do not…
We consider quantum walks on a finite graphs to which infinite tails are attached. We explore how the propagating and bound states depend on the structure of the finite graph. The S-matrix for such graphs is defined. Its unitarity is proved…
Recently, Keating and the second author of this paper devised a heuristic for predicting asymptotic formulas for moments of the Riemann zeta-function $\zeta(s)$. Their approach indicates how lower twisted moments of $\zeta(s)$ may be used…
Chinta, Jorgenson and Karlsson introduced a generalized version of the determinant formula for the Ihara zeta function associated to finite or infinite regular graphs. On the other hand, Konno and Sato obtained a formula of the…
We introduce and analyze a one-dimensional quantum walk with two time-independent rotations on the coin. We study the influence on the property of quantum walk due to the second rotation on the coin. Based on the asymptotic solution in the…
A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. Searching in this mathematical framework has interested the community since a long time. However, most results consider spatial search…
A continuous-time quantum walk on a dynamic graph evolves by Schr\"odinger's equation with a sequence of Hamiltonians encoding the edges of the graph. This process is universal for quantum computing, but in general, the dynamic graph that…
We establish the theory for pretty good state transfer in discrete-time quantum walks. For a class of walks, we show that pretty good state transfer is characterized by the spectrum of certain Hermitian adjacency matrix of the graph; more…
We propose a class of continuous-time quantum walk models on graphs induced by a certain class of discrete-time quantum walk models with the parameter $\epsilon\in [0,1]$. Here the graph treated in this paper can be applied both finite and…
We consider the dynamical properties of dissipative continuous-time quantum walks on directed graphs. Using a large-deviation approach we construct a thermodynamic formalism allowing us to define a dynamical order parameter, and to identify…