Related papers: Quantum walks on simplexes and multiple perfect st…
We present an investigation of many-particle quantum walks in systems of non-interacting distinguishable particles. Along with a redistribution of the many-particle density profile we show that the collective evolution of the many-particle…
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…
We give a new formula for computing the isospectral reduction of a matrix (and graph) down to a submatrix (or subgraph). Using this, we generalize the notion of isospectral reductions. In addition, we give a procedure for constructing a…
Non-local higher-energy auxiliary states have been successfully used to entangle pairs of qubits in different quantum computing systems. Typically a longer-span non-local state or sequential application of few-qubit entangling gates are…
Quantum walks are widely and successfully used to model diverse physical processes. This leads to computation of the models, to explore their properties. Quantum walks have also been shown to be universal for quantum computing. This is a…
We present a generalized definition of discrete-time quantum walks convenient for capturing a rather broad spectrum of walker's behavior on arbitrary graphs. It includes and covers both: the geometry of possible walker's positions with…
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…
In this paper, we propose an extension of quantum searches on graphs driven by quantum walks to simplicial complexes. To this end, we newly define a quantum walk on simplicial complex which is an alternative of preceding studies by authors.…
We study the transition matrix of a quantum walk on strongly regular graphs. It is proposed by Emms, Hancock, Severini and Wilson in 2006, that the spectrum of $S^+(U^3)$, a matrix based on the amplitudes of walks in the quantum walk,…
Recently, quantized versions of random walks have been explored as effective elements for quantum algorithms. In the simplest case of one dimension, the theory has remained divided into the discrete-time quantum walk and the continuous-time…
The study of quantum walks has been shown to have a wide range of applications in areas such as artificial intelligence, the study of biological processes, and quantum transport. The quantum stochastic walk, which allows for incoherent…
We consider two independent quantum walks on separate lines augmented by partial or full swapping of coins after each step. For classical random walks, swapping or not swapping coins makes little difference to the random walk…
Quantum walks have emerged as a transformative paradigm in quantum information processing and can be applied to various graph problems. This study explores discrete-time quantum walks on simplicial complexes, a higher-order generalization…
We consider an analogue of the well-known Riemann Hypothesis based on quantum walks on graphs with the help of the Konno-Sato theorem. Furthermore, we give some examples for complete, cycle, and star graphs.
We discuss spreading estimates for dynamical systems given by the iteration of an extended CMV matrix. Using a connection due to Cantero--Gr\"unbaum--Moral--Vel\'azquez, this enables us to study spreading rates for quantum walks in one…
The transfer of quantum information between different locations is key to many quantum information processing tasks. Whereas, the transfer of a single qubit state has been extensively investigated, the transfer of a many-body system…
We demonstrate that continuous time quantum walks on several types of branching graphs, including graphs with loops, are identical to quantum walks on simpler linear chain graphs. We also show graph types for which such equivalence does not…
Quantum walks are considered to be quantum counterparts of random walks.They show us impressive probability distributions which are different from those of random walks.That fact has been precisely proved in terms of mathematics and some of…
We clarify the relations between the mathematical structures that enable fashioning quantum walks on regular graphs and their realizations in anyonic systems. Our protagonist is association schemes that may be synthesized from type-II…
A quantum walk model which reflects the $2$-cell embedding on the orientable closed surface of a graph in the dynamics is introduced. We show that the scattering matrix is obtained by finding the faces on the underlying surface which have…