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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…

Quantum Physics · Physics 2022-09-27 Quancheng Liu , David A. Kessler , Eli Barkai

This paper presents a deterministic search algorithm on complete bipartite graphs. Our algorithm adopts the simple form of alternating iterations of an oracle and a continuous-time quantum walk operator, which is a generalization of…

Quantum Physics · Physics 2024-05-13 Honghong Lin , Yun Shang

Quantum walk algorithms can speed up search of physical regions of space in both the discrete-time [arXiv:quant-ph/0402107] and continuous-time setting [arXiv:quant-ph/0306054], where the physical region of space being searched is modeled…

Quantum Physics · Physics 2019-10-08 Jeremy Cook

Quantum walks play an important role in the area of quantum algorithms. Many interesting problems can be reduced to searching marked states in a quantum Markov chain. In this context, the notion of quantum hitting time is very important,…

Quantum Physics · Physics 2009-12-08 R. A. M. Santos , R. Portugal

We investigate the behavior of coherence in scattering quantum walk search on complete graph under the condition that the total number of vertices of the graph is greatly larger than the marked number of vertices we are searching, $N \gg…

Quantum Physics · Physics 2020-03-19 Yun-Long Su , Si-Yuan Liu , Xiao-Hui Wang , Heng Fan , Wen-Li Yang

Grover's quantum search algorithm provides a way to speed up combinatorial search, but is not directly applicable to searching a physical database. Nevertheless, Aaronson and Ambainis showed that a database of N items laid out in d spatial…

Quantum Physics · Physics 2007-05-23 Andrew M. Childs , Jeffrey Goldstone

Quantum walk is a potent technique for building quantum algorithms. This paper examines the quantum walk search algorithm on complete multipartite graphs with multiple marked vertices, which has not been explored before. Two specific cases…

Quantum Physics · Physics 2024-10-08 Ningxiang Chen , Meng Li , Xiaoming Sun

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…

Quantum Physics · Physics 2023-12-27 Mathieu Roget , Giuseppe Di Molfetta

Node connectivity plays a central role in temporal network analysis. We provide a comprehensive study of various concepts of walks in temporal graphs, that is, graphs with fixed vertex sets but edge sets changing over time. Taking into…

Data Structures and Algorithms · Computer Science 2020-03-12 Anne-Sophie Himmel , Matthias Bentert , André Nichterlein , Rolf Niedermeier

One of the significant breakthroughs in quantum computation is Grover's algorithm for unsorted database search. Recently, the applications of Grover's algorithm to solve global optimization problems have been demonstrated, where unknown…

Quantum Physics · Physics 2017-11-22 Yan Wang

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…

Quantum Physics · Physics 2024-03-15 Ilaria Gianani , Claudia Benedetti

We consider the quantum search problem with a continuous time quantum walk for networks of finite spectral dimension d_{s} of the network Laplacian. For general networks of fractal (integer or non-integer) dimension d_{f}, for which in…

Quantum Physics · Physics 2017-03-08 Shanshan Li , Stefan Boettcher

In this paper, we consider a continuous-time quantum walk based search algorithm. We introduce equitable partition of the graph and perfect state transfer on it. By these two methods, we can calculate the success probability and the finding…

Quantum Physics · Physics 2022-09-19 Yusuke Ide , Akihiro Narimatsu

This article presents a novel and succinct algorithmic framework via alternating quantum walks, unifying quantum spatial search, state transfer and uniform sampling on a large class of graphs. Using the framework, we can achieve exact…

Quantum Physics · Physics 2025-04-22 Qingwen Wang , Ying Jiang , Lvzhou Li

Given the extensive application of classical random walks to classical algorithms in a variety of fields, their quantum analogue in quantum walks is expected to provide a fruitful source of quantum algorithms. So far, however, such…

Quantum Physics · Physics 2008-03-26 B. L. Douglas , J. B. Wang

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…

Quantum Physics · Physics 2015-07-02 Iain Foulger , Sven Gnutzmann , Gregor Tanner

In the typical spatial search problems solved by continuous-time quantum walk, changing the location of the marked vertices does not alter the search problem. In this paper, we consider search when this is no longer true. In particular, we…

Quantum Physics · Physics 2016-04-11 Thomas G. Wong

We show how to search N items arranged on a $\sqrt{N}\times\sqrt{N}$ grid in time $O(\sqrt N \log N)$, using a discrete time quantum walk. This result for the first time exhibits a significant difference between discrete time and continuous…

Quantum Physics · Physics 2007-05-23 Andris Ambainis , Julia Kempe , Alexander Rivosh

Continuous-time quantum walks are natural tools for spatial search, where one searches for a marked vertex in a graph. Sometimes, the structure of the graph causes the walker to get trapped, such that the probability of finding the marked…

Quantum Physics · Physics 2016-08-10 Thomas G. Wong , Pascal Philipp

The coined quantum walk is a discretization of the Dirac equation of relativistic quantum mechanics, and it is the basis of many quantum algorithms. We investigate how it searches the complete bipartite graph of $N$ vertices for one of $k$…

Quantum Physics · Physics 2019-03-04 Mason L. Rhodes , Thomas G. Wong