Related papers: Why and how to add direction to a quantum walk
This paper discusses continuous-time quantum walks and asymptotic state transfer in graphs with an involution. By providing quantitative bounds on the eigenvectors of the Hamiltonian, it provides an approach to achieving high-fidelity state…
We explore theoretically how the coupling to cavity vacuum fields affects the electron transport in quantum conductors due to the counter-rotating-wave terms of light-matter interaction. We determine the quantum conductance in terms of the…
A pointed graph $(\Gamma,v_0)$ induces a family of transition matrices in Wildberger's construction of a hermitian hypergroup via a random walk on $\Gamma$ starting from $v_0$. We will give a necessary condition for producing a hermitian…
We formulate three current models of discrete-time quantum walks in a combinatorial way. These walks are shown to be closely related to rotation systems and 1-factorizations of graphs. For two of the models, we compute the traces and total…
We investigate the global chirality distribution of the quantum walk on the line when decoherence is introduced either through simultaneous measurements of the chirality and particle position, or as a result of broken links. The first…
In this paper we analyze the ground state phase diagram of a class of fermionic Hamiltonians by looking at the fidelity of ground states corresponding to slightly different Hamiltonian parameters. The Hamiltonians under investigation can be…
A multi-branch quantum circuit is considered from the viewpoint of coherent electron or wave transport. Starting with the closed system, we give analytical conditions for the appearance of two isolated localized states out of the energy…
The interest in quantum walks has been steadily increasing during the last two decades. It is still worth to present new forms of quantum walks that might find practical applications and new physical behaviors. In this work, we define…
The theory of random walks on finite graphs is well developed with numerous applications. In quantum walks, the propagation is governed by quantum mechanical rules; generalizing random walks to the quantum setting. They have been…
Quantum mechanics still provides new unexpected effects when considering the transport of energy and information. Models of continuous time quantum walks, which implicitly use time-reversal symmetric Hamiltonians, have been intensely used…
We present an introduction to coined quantum walks on regular graphs, which have been developed in the past few years as an alternative to quantum Fourier transforms for underpinning algorithms for quantum computation. We then describe our…
We address the question of symmetries of an important type of quantum walks. We introduce all the necessary definitions and provide a rigorous formulation of the problem. Using a thorough analysis, we reach the complete answer by presenting…
In recent years, new neural network architectures designed to operate on graph-structured data have pushed the state-of-the-art in the field. A large set of these architectures utilize a form of classical random walks to diffuse…
It is shown that an undirected graph $G$ is cospectral with the Hermitian adjacency matrix of a mixed graph $D$ obtained from a subgraph $H$ of $G$ by orienting some of its edges if and only if $H=G$ and $D$ is obtained from $G$ by a…
Incorporating higher-order interactions in information processing enables us to build more accurate models, gain deeper insights into complex systems, and address real-world challenges more effectively. However, existing methods, such as…
A continuous-time quantum walk on a graph $X$ is represented by the complex matrix $\exp (-\mathrm{i} t A)$, where $A$ is the adjacency matrix of $X$ and $t$ is a non-negative time. If the graph models a network of interacting qubits,…
The presence of disorder and inhomogeneities in quantum networks has often been unexpectedly beneficial for both quantum and classical resources. Here, we experimentally realize a controllable inhomogenous Quantum Walk dynamics, which can…
Entanglement, one of the clearest manifestations of non-classical physics, holds significant promise for technological applications such as more secure communications and faster computations. In this paper we explore the use of…
We present a review on the progress in the understanding and characterization of holonomy and topology of a discrete-time quantum walk architecture, consisting of a unitary step given by a sequence of two non-commuting rotations in…
The non-Hermitian Hamiltonian describes the effective dynamics of a system coupled to a continuously measured bath, and can exhibit anti-unitary symmetries that give rise to exceptional points and broken phases with complex eigenvalues,…