相关论文: Orthogonal Polynomials and Perfect State Transfer

We describe fast algorithms for approximating the connection coefficients between a family of orthogonal polynomials and another family with a polynomially or rationally modified measure. The connection coefficients are computed via…

We examine conditions for a pair of strongly cospectral vertices to have pretty good quantum state transfer in terms of minimal polynomials, and provide cases where pretty good state transfer can be ruled out. We also provide new examples…

In this paper, we will discuss the notion of almost orthogonality in a functional sequence.Especially, we will define a few sequences of almost orthogonal polynomials which can be used successfully for modeling of electronic systems which…

We discuss the implementation of optical quantum networks where the interface between stationary and photonic qubits is realized by optomechanical transducers [K. Stannigel et al., PRL 105, 220501 (2010)]. This approach does not rely on the…

The existence of perfect state transfer (PST) on quantum spin networks is a fundamental problem in mathematics and physics. Various works in the literature have explored PST in graphs with arithmetic origins, such as gcd-graphs over…

In the quest for designing novel protocols for quantum information and quantum computation, an important goal is to achieve perfect quantum state transfer for systems beyond the well-known one dimensional cases, such as 1d spin chains. We…

We review properties of q-orthogonal polynomials, related to their orthogonality, duality and connection with the theory of symmetric (self-adjoint) operators, represented by a Jacobi matrix. In particular, we show how one can naturally…

Transferring quantum states efficiently between distant nodes of an information processing circuit is of paramount importance for scalable quantum computing. We report on the first observation of a perfect state transfer protocol on a…

Perfect state transfer (PST) has great significance due to its applications in quantum information processing and quantum computation. In this paper we present a characterization on connected simple Cayley graph $\Gamma={\rm Cay}(G,S)$…

Connections between the 1-excitation dynamics of spin lattices and quantum walks on graphs will be surveyed. Attention will be paid to perfect state transfer (PST) and fractional revival (FR) as well as to the role played by orthogonal…

A programmable quantum networks model is used in this paper for development of methods of control of a quantum state transport. These methods may be applied for a wide variety of patterns of controlled state transmission and spreading in…

We consider the representation of a continuous-time quantum walk in a graph $X$ by the matrix $\exp(itA(X))$. We provide necessary and sufficient criteria for distance-regular graphs and, more generally, for graphs in association schemes to…

This paper is a short introduction to orthogonal polynomials, both the general theory and some special classes. It ends with some remarks about the usage of computer algebra for this theory.

We study perfect state transfer of quantum walks on signed graphs. Our aim is to show that negative edges are useful for perfect state transfer. Specific results we prove include: (1) The signed join of a negative 2-clique with any positive…

The issue of quantum states' transfer -- in particular, for so-called Perfect State Transfer (PST) -- in the networks represented by the spin chains seems to be one of the major concerns in quantum computing. Especially, in the context of…

A duality between the properties of many spinor bosons on a regular lattice and those of a single particle on a weighted graph reveals that a quantum particle can traverse an infinite hierarchy of networks with perfect probability in…

This paper revisits the notion of classical orthogonal polynomials from a broader functional-analytic point of view. It is intended neither as a survey of known results nor as a review of the literature, but rather as a conceptual…

In this paper we build on the ideas presented in previous works for perfectly transferring a quantum state between opposite ends of a spin chain using a fixed Hamiltonian. While all previous studies have concentrated on nearest-neighbor…

The subject of this paper is a kind of dynamical systems called quantum walks. We study one-dimensional homogeneous analytic quantum walks U. We explain how to identify the space of all the uniform intertwining operators between these…

By using the properties of orthogonal polynomials, we present an exact unitary transformation that maps the Hamiltonian of a quantum system coupled linearly to a continuum of bosonic or fermionic modes to a Hamiltonian that describes a…