Related papers: Quantitative approach to Grover's quantum walk on …
We analyze a continuous-time quantum walk on a chimera graph, which is a graph of choice for designing quantum annealers, and we discover beautiful quantum-walk features such as localization that starkly distinguishes classical from quantum…
In quantum computing, the quantum walk search algorithm is designed for locating fixed marked nodes within a graph. However, when multiple marked nodes exist, the conventional search algorithm lacks the capacity to simultaneously amplify…
A quantum walk on a lattice is a paradigm of a quantum search in a database. The database qubit strings are the lattice sites, qubit rotations are tunneling events, and the target site is tagged by an energy shift. For quantum walks on a…
Quantum walks have been very successful in the development of search algorithms in quantum information, in particular in the development of spatial search algorithms. However, the construction of continuous-time quantum search algorithms in…
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…
We study continuous-time quantum walks mimicking the quantum search based on Grover's procedure. This allows us to consider structures, that is, databases, with arbitrary topological arrangements of their entries. We show that the…
Continuous time quantum walks provide an important framework for designing new algorithms and modelling quantum transport and state transfer problems. Often, the graph representing the structure of a problem contains certain symmetries that…
Spatial search is an important problem in quantum computation, which aims to find a marked vertex on a graph. We propose a novel approach for designing deterministic quantum search algorithms on a variety of graphs via alternating quantum…
To investigate the performance of quantum information tasks on networks whose topology changes in time, we study the spatial search algorithm by continuous time quantum walk to find a marked node on a random temporal network. We consider a…
We review some of quantum algorithms for search problems: Grover's search algorithm, its generalization to amplitude amplification, the applications of amplitude amplification to various problems and the recent quantum algorithms based on…
A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. Searching in this mathematical framework has interested the community since a long time. However, most results consider spatial search…
The graph isomorphism problem asks whether two graphs are identical up to vertex relabeling. While the exact problem admits quasi-polynomial-time classical algorithms, many applications in molecular comparison, noisy network analysis, and…
We address quantum spatial search on graphs and its implementation by continuous-time quantum walks in the presence of dynamical noise. In particular, we focus on search on the complete graph and on the star graph of order $N$, proving that…
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 introduce a simple diagrammatic approach for estimating how a randomly walking quantum particle searches on a graph in continuous-time, which involves sketching small weighted graphs with self-loops and considering degenerate…
We establish a lower bound concerning the computational complexity of Grover's algorithms on fractal networks. This bound provides general predictions for the quantum advantage gained for searching unstructured lists. It yields a…
The Grover walk is one of the most well-studied quantum walks on graphs. In this paper, we investigate its periodicity to reveal the relationship between the quantum walk and the underlying graph, focusing particularly on the…
Dynamic programming is a cornerstone of graph-based optimization. While effective, it scales unfavorably with problem size. In this work, we present QuantGraph, a two-stage quantum-enhanced framework that casts local and global…
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…
This comment is to correct the proof of optimality of quantum spatial search for Erd\H{o}s-R\'enyi graphs presented in `Spatial Search by Quantum Walk is Optimal for Almost all Graphs' (https://doi.org/10.1103/PhysRevLett.116.100501). The…