scholarly journals Quantum Walk Algorithm for Element Distinctness

Author(s):  
A. Ambainis
Keyword(s):  
2007 ◽  
Vol 37 (1) ◽  
pp. 210-239 ◽  
Author(s):  
Andris Ambainis
Keyword(s):  

2020 ◽  
Vol 19 (5) ◽  
Author(s):  
Prateek Chawla ◽  
Roopesh Mangal ◽  
C. M. Chandrashekar

2005 ◽  
Vol 5 (7) ◽  
pp. 593-604
Author(s):  
A.M. Childs ◽  
J.M. Eisenberg

Recently, Ambainis gave an $O(N^{2/3})$-query discrete-time quantum walk algorithm for the element distinctness problem, and more generally, an $O(N^{L/(L+1)})$-query algorithm for finding $L$ equal numbers. We review this algorithm and give a simplified and tightened analysis of its query complexity using techniques previously applied to the analysis of continuous-time quantum walk. We also briefly discuss applications of the algorithm and pose two open problems regarding continuous-time quantum walk and lower bounds.


2019 ◽  
Vol 17 (07) ◽  
pp. 1950060
Author(s):  
Pulak Ranjan Giri ◽  
Vladimir Korepin

Hanoi network (HN) has a one-dimensional periodic lattice as its main structure with additional long-range edges, which allow having efficient quantum walk algorithm that can find a target state on the network faster than the exhaustive classical search. In this paper, we use regular quantum walks and lackadaisical quantum walks, respectively, to search for a target state. From the curve fitting of the numerical results for HN of degrees three and four, we find that their running time for the regular quantum walks are followed by amplitude amplification scales as [Formula: see text] and [Formula: see text], respectively. For the search by lackadaisical quantum walks, the running time scales are as [Formula: see text] and [Formula: see text], respectively.


2021 ◽  
Vol 103 (6) ◽  
Author(s):  
G. A. Bezerra ◽  
P. H. G. Lugão ◽  
R. Portugal

APL Photonics ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 020802
Author(s):  
Alessio D’Errico ◽  
Raouf Barboza ◽  
Rebeca Tudor ◽  
Alexandre Dauphin ◽  
Pietro Massignan ◽  
...  
Keyword(s):  

Sign in / Sign up

Export Citation Format

Share Document