Related papers: Quantum Walks with Gremlin
A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science.…
Quantum walks underlie an important class of quantum computing algorithms, and represent promising approaches in various simulations and practical applications. Here we design stroboscopically monitored quantum walks and their subsequent…
The study of quantum walk processes has been widely divided into two standard variants, the discrete-time quantum walk (DTQW) and the continuous-time quantum walk (CTQW). The connection between the two variants has been established by…
We study the simulation of the topological phases in three subsequent dimensions with quantum walks. We are mainly focused on the completion of a table for the protocols of the quantum walk that could simulate different family of the…
The characterization of the Hamiltonian parameters defining a quantum walk is of paramount importance when performing a variety of tasks, from quantum communication to computation. When dealing with physical implementations of quantum…
In this paper we unveil some features of a discrete-time quantum walk on the line whose coin depends on the temporal variable. After considering the most general form of the unitary coin operator, we focus on the role played by the two…
Quantum walks can be used either as tools for quantum algorithm development or as entanglement generators, potentially useful to test quantum hardware. We present a novel algorithm based on a discrete Hadamard quantum walk on a line with…
We construct a new type of quantum walks on simplicial complexes as a natural extension of the well-known Szegedy walk on graphs. One can numerically observe that our proposing quantum walks possess linear spreading and localization as in…
We set the criteria under which superposition of causal order can be incorporated in to quantum walks. In particular, we show that only periodic quantum walks or those with at least one disorder exhibit Superposition of causal order under…
We present a discrete-time, one-dimensional quantum walk based on the entanglement between the momentum of ultracold rubidium atoms (the walk space) and two internal atomic states (the "coin" degree of freedom). Our scheme is highly…
We define a discrete-time, coined quantum walk on weighted graphs that is inspired by Szegedy's quantum walk. Using this, we prove that many lackadaisical quantum walks, where each vertex has $l$ integer self-loops, can be generalized to a…
We present a new scheme for a discrete-time quantum walk on two- and three-dimensional lattices using a two-state particle. We use different Pauli basis as translational eigestates for different axis and show that the coin operation, which…
Simulation and programming of current quantum computers as Noisy Intermediate-Scale Quantum (NISQ) devices represent a hot topic at the border of current physical and information sciences. The quantum walk process represents a basic…
Quantum walks are a promising framework that can be used to both understand and implement quantum information processing tasks. The quantum stochastic walk is a recently developed framework that combines the concept of a quantum walk with…
The connection between coined and continuous-time quantum walk models has been addressed in a number of papers. In most of those studies, the continuous-time model is derived from coined quantum walks by employing dimensional reduction and…
The quantum walk dynamics obey the laws of quantum mechanics with an extra locality constraint, which demands that the evolution operator is local in the sense that the walker must visit the neighboring locations before endeavoring to…
Many phenomena in solid-state physics can be understood in terms of their topological properties. Recently, controlled protocols of quantum walks are proving to be effective simulators of such phenomena. Here we report the realization of a…
The development of Graph Neural Networks (GNNs) has led to great progress in machine learning on graph-structured data. These networks operate via diffusing information across the graph nodes while capturing the structure of the graph.…
We study whether the probability distribution of a discrete quantum walk can get arbitrarily close to uniform, given that the walk starts with a uniform superposition of the outgoing arcs of some vertex. We establish a characterization of…
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…