相关论文: Orthogonal Polynomials and Perfect State Transfer

In recent years, significant progress has been made in the field of state transfer in spin chains, with the aim of achieving perfect state transfer for quantum information processing applications. Previous research has mainly focused on…

The graph isomorphism problem is theoretically interesting and also has many practical applications. The best known classical algorithms for graph isomorphism all run in time super-polynomial in the size of the graph in the worst case. An…

We investigate the quantum state transfer in a chain of particles satisfying q-deformed oscillators algebra. This general algebraic setting includes the spin chain and the bosonic chain as limiting cases. We study conditions for perfect…

Quantum walks on graphs are ubiquitous in quantum computing finding a myriad of applications. Likewise, random walks on graphs are a fundamental building block for a large number of algorithms with diverse applications. While the…

We investigate quantum state transfer on a class of bipartite graphs, namely the butterfly graphs, within the framework of discrete-time quantum walks. These graphs facilitate the construction of scalable quantum networks that enable…

Let $\{P_n \}_{n\ge0}$ be a sequence of monic orthogonal polynomials with respect to a quasi--definite linear functional $u$ and $\{Q_n \}_{n\ge0}$ a sequence of polynomials defined by $$Q_n(x)=P_n(x)+s_n P_{n-1}(x)+t_n P_{n-2}(x),\quad…

This paper discusses operators lowering or raising the degree but preserving the parameters of special orthogonal polynomials. Results for one-variable classical (q-)orthogonal polynomials are surveyed. For Jacobi polynomials associated…

The interest in orthogonal polynomials and random Fourier series in numerous branches of science and a few studies on random Fourier series in orthogonal polynomials inspired us to focus on random Fourier series in Jacobi polynomials. In…

Rational function approximations find applications in many areas including macro-modeling of high-frequency circuits, model order reduction for controller design, interpolation and extrapolation of system responses, surrogate models for…

A general procedure for constructing coherent states, which are eigenstates of annihilation operators, related to quantum mechanical potential problems, is presented. These coherent states, by construction are not potential specific and…

Quantum states evolving at equidistant steps into a set of mutually orthogonal states of finite or infinite cardinality p exhibit an interesting physical effect. The analysis of the amplitudes of the state at half the step time with the…

A survey of recents advances in the theory of Heun operators is offered. Some of the topics covered include: quadratic algebras and orthogonal polynomials, differential and difference Heun operators associated to Jacobi and Hahn…

For a quantum walk on a graph, there exist many kinds of operators for the discrete-time evolution. We give a general relation between the characteristic polynomial of the evolution matrix of a quantum walk on edges and that of a kind of…

Quantum effects are known to provide an advantage in particle transfer across networks. In order to achieve this advantage, requirements on both a graph type and a quantum system coherence must be found. Here we show that the process of…

Polynomials known as Multiple Orthogonal Polynomials in a single variable are polynomials that satisfy orthogonality conditions concerning multiple measures and play a significant role in several applications such as Hermite-Pad\'e…

The transfer of a quantum state between distant nodes in two-dimensional networks, is considered. The fidelity of state transfer is calculated as a function of the number of interactions in networks that are described by regular graphs. It…

The paper investigates perfect state transfer (PST) in Grover walks on Cayley graphs over the dihedral group $D_n$. The Grover walk is a discrete-time quantum walk widely studied in quantum information processing. A Cayley graph…

For any graph $X$ with the adjacency matrix $A$, the transition matrix of the continuous-time quantum walk at time $t$ is given by the matrix-valued function $\mathcal{H}_X(t)=\mathrm{e}^{itA}$. We say that there is perfect state transfer…

This work recollects a non-universal set of quantum gates described by higher-dimensional Spin groups. They are also directly related with matchgates in theory of quantum computations and complexity. Various processes of quantum state…

We introduce a new tool for quantum algorithms called quantum fast-forwarding (QFF). The tool uses quantum walks as a means to quadratically fast-forward a reversible Markov chain. More specifically, with $P$ the Markov chain transition…