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Search via Quantum Walk

Frédéric Magniez, Ashwin Nayak, Jérémie Roland, Miklos Santha
2011 SIAM journal on computing (Print)  
We propose a new method for designing quantum search algorithms for finding a "marked" element in the state space of a classical Markov chain.  ...  The algorithm is based on a quantum walk \'a la Szegedy (2004) that is defined in terms of the Markov chain.  ...  From quantum walk to search Outline of search algorithm We now describe a search algorithm that may be viewed as a quantum analogue of Search Algorithm 1 of Section 1.2.  ... 
doi:10.1137/090745854 fatcat:n2k3kqgktrg2zj3cyfbjfyf6du

Search via Quantum Walk [chapter]

Jiangfeng Du, Chao Lei, Gan Qin, Dawei Lu, Xinhua Peng
2011 Search Algorithms and Applications  
The structure of this chapter is as follows, section 2 is the introduction of the quantum walk, including the coined and continuous quantum walk; section 3 is the search algorithm via quantum walk, for  ...  In this chapter we will focus on the search algorithm based on quantum walk.  ...  Search via Quantum Walk, Search Algorithms and Applications, Prof.  ... 
doi:10.5772/15814 fatcat:avtvzjllovc77jkr5jf4knuwi4

Searching via nonlinear quantum walk on the 2D-grid [article]

Basile Herzog, Giuseppe Di Molfetta
2020 arXiv   pre-print
We provide numerical evidence that the nonlinear searching algorithm introduced by Wong and Meyer , rephrased in terms of quantum walks with effective nonlinear phase, can be extended to the finite 2-dimensional  ...  We also proved that there exists an optimal choice of the walker parameters to avoid that the time measurement precision affects the complexity searching time of the algorithm.  ...  Nonlinearity in Quantum Walks have been considered in several recent studies and may appear either under the form of nonlinear phases, (e.g. in Kerr medium [21] and [22] ) or via a feed-forward quantum  ... 
arXiv:2009.07800v3 fatcat:jc3al7if5jb4ngtr37knm6b6ni

Search via quantum walks with intermediate measurements

Efrain Buksman, André L. Fonseca de Oliveira, Jesús García López de Lacalle
2015 International Journal of Modern Physics B  
A modification of Tulsi's quantum search algorithm with intermediate measurements of the control is presented.  ...  In order to analyze the effect of measurements in quantum searches, a different choice of the angular parameter is used.  ...  This quantum walk depends on an angular parameter S, where the optimum valué ensures an order of 0(y/NlogN), considering a *JÑ X y/Ñ search grid.  ... 
doi:10.1142/s0217979215501271 fatcat:rmjcrjzzdjf4hicq4ufxfh5rrm

Role of symmetry in quantum search via continuous-time quantum walk [article]

Yunkai Wang, Shengjun Wu
2021 arXiv   pre-print
For quantum search via the continuous-time quantum walk, the evolution of the whole system is usually limited in a small subspace.  ...  search.  ...  For quantum search via the continuous-time quantum walk, the evolution of the whole system is usually limited in a small subspace.  ... 
arXiv:2106.08398v1 fatcat:a7b5rjoxqncrzoru3jbqasdkoa

Resolving degeneracies in Google search via quantum stochastic walks [article]

Naini Dudhe, Colin Benjamin
2022 arXiv   pre-print
We employ quantum stochastic walks (QSW) with the hope of bettering the classical PageRank (CPR) algorithm, which is based on classical continuous time random walks (CTRW).  ...  Among them, Google is the most widely used search engine. The PageRank algorithm is the backbone of Google search, ranking web pages according to relevance and recency.  ...  Quantum stochastic walks and quantum PageRank Quantum stochastic walk (QSW) is the hybrid version of CTRW and CTQW and was introduced in Ref. [11] .  ... 
arXiv:2207.11429v1 fatcat:gy3ax7cwizhl5cpwmsbi3vpdze

Searching via Nonlinear Quantum Walk on the 2D-Grid

Giuseppe Di Molfetta, Basile Herzog
2020 Algorithms  
We provide numerical evidence that the nonlinear searching algorithm introduced by Wong and Meyer, rephrased in terms of quantum walks with effective nonlinear phase, can be extended to the finite 2-dimensional  ...  We also proved that there exists an optimal choice of the walker parameters to avoid the time measurement precision affecting the complexity searching time of the algorithm.  ...  Nonlinearity in quantum walks has been considered in several recent studies and may appear either under the form of nonlinear phases (e.g., in Kerr medium [19, 20] ) or via a feed-forward quantum diffusion  ... 
doi:10.3390/a13110305 fatcat:azcwnvv4jfaglnsr2zyczlxxde

Searching via walking: How to find a marked clique of a complete graph using quantum walks

Mark Hillery, Daniel Reitzner, Vladimír Bužek
2010 Physical Review A. Atomic, Molecular, and Optical Physics  
This leads to a quantum search that is quadratically faster than a corresponding classical search.  ...  We employ a version of a quantum walk, the scattering walk, which lends itself to experimental implementation.  ...  In particular, quantum walks have been used to investigate searches on a number of different graphs.  ... 
doi:10.1103/physreva.81.062324 fatcat:lk2kwjjbrfe7vbjj7pm2tqluw4

Reducing number of gates in quantum random walk search algorithm via modification of coin operators [article]

Hristo Tonchev, Petar Danev
2022 arXiv   pre-print
This paper examines a way to simplify the circuit of quantum random walk search algorithm, when the traversing coin is constructed by both generalized Householder reflection and an additional phase multiplier  ...  It is shown explicitly how to construct such walk coin in order to obtain more robust quantum algorithm.  ...  for finding triangles [10] and quantum random walk search (QRWS) [11] .  ... 
arXiv:2204.12858v1 fatcat:kdvfb34pmzcdrd3zmxdnq3thku

Spatial search via non-linear quantum walk [article]

Mahdi Ebrahimi Kahou, University Of Calgary, University Of Calgary, David Feder
2013
One approach to the development of quantum search algorithms is the quantum walk.  ...  In this thesis we investigate the role of non-linearity in determining the efficiency of the spatial search algorithm within the quantum walk model, for the complete graph.  ...  Chapter 3 Non-linear continuous-time quantum walk In the previous chapter I showed that spatial search via a continuous-time quantum walk with one quantum walker on a complete graph provides a quadratic  ... 
doi:10.11575/prism/27845 fatcat:n4q2uoyn2vhcbhlmh4cv7xvl2e

Implementing graph-theoretic quantum algorithms on a silicon photonic quantum walk processor

Xiaogang Qiang, Yizhi Wang, Shichuan Xue, Renyou Ge, Lifeng Chen, Yingwen Liu, Anqi Huang, Xiang Fu, Ping Xu, Teng Yi, Fufang Xu, Mingtang Deng (+6 others)
2021 Science Advances  
We apply the device to quantum walk algorithms for searching vertices in graphs and testing for graph isomorphisms.  ...  This opens the way to large-scale, programmable quantum walk processors for classically intractable applications.  ...  include searching on circulant graphs (25) and searching via multiboson CTQWs (18) .  ... 
doi:10.1126/sciadv.abb8375 pmid:33637521 fatcat:xusuyu2nyfhzrdjik6sx2jrrfu

Quantum Severalty: Speed-up and Suppress Effect in Searching Problem [article]

Jin-Hui Zhu, Li-Hua Lu, You-Quan Li
2019 arXiv   pre-print
We report new findings of speed-up and suppression effects occuring in the quantum search problem through the study of quantum walk on a graph with floating vertices.  ...  This is expected to provide new ideas for quantum simulation by means of qubit chips.  ...  (B) Experiment scheme for quantum walk via optical fibre.  ... 
arXiv:1909.06798v1 fatcat:ubxfiq7vkbb6vjyy37smlnck3y

Complexity analysis of quantum walk based search algorithms [article]

B. L. Douglas, J. B. Wang
2014 arXiv   pre-print
We present several families of graphs that allow both efficient quantum walk implementations and efficient quantum walk based search algorithms.  ...  For these graphs, we construct quantum circuits that explicitly implement the full quantum walk search algorithm, without reference to a 'black box' oracle.  ...  QUANTUM WALK BASED SEARCH Quantum walks can be thought of as the quantum analogues of classical random walks.  ... 
arXiv:1408.1616v1 fatcat:wdr3mjksaveibkmbtnkr2mkmlq

Improved Quantum Algorithm for Triangle Finding via Combinatorial Arguments

Francois Le Gall
2014 2014 IEEE 55th Annual Symposium on Foundations of Computer Science  
Magniez, Santha and Szegedy [12], using quantum walk search, constructed a quantum algorithm for triangle finding with improved query complexityÕ(n 13/10 ).  ...  Besides Grover search and quantum walks, a third technique to design quantum query algorithms appeared recently when Reichardt [14] proved that the quantum query complexity of a problem can be found by  ...  To deal with this problem, we use a quantum walk over a Johnson graph, which enables us to implement the construction of ∆ G (X, B, w) concurrently to the search of B and w.  ... 
doi:10.1109/focs.2014.31 dblp:conf/focs/Gall14 fatcat:wlyckj5parcw5l5b7nhhj4jfjm

Deterministic spatial search using alternating quantum walks [article]

S. Marsh, J. B. Wang
2021 arXiv   pre-print
This paper examines the performance of spatial search where the Grover diffusion operator is replaced by continuous-time quantum walks on a class of interdependent networks.  ...  We prove that for a set of optimal quantum walk times and marked vertex phase shifts, a deterministic algorithm for structured spatial search is established that finds the marked vertex with 100% probability  ...  INTRODUCTION Quantum search on a spatially structured database via a continuous-time quantum walk (CTQW) is an important and broad problem in quantum computation [1] [2] [3] [4] [5] , which aims to find  ... 
arXiv:2104.03806v1 fatcat:be5kzhgz7jdv7ngncncuegienu
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