scholarly journals Quantum Walk Algorithm for Element Distinctness

2004 ◽  
Author(s):  
A. Ambainis
Keyword(s):  
Quantum Walk ◽  
Walk Algorithm

scholarly journals Quantum Walk Algorithm for Element Distinctness

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

scholarly journals Discrete-time quantum walk algorithm for ranking nodes on a network

2020 ◽  
Vol 19 (5) ◽  
Author(s):  
Prateek Chawla ◽  
Roopesh Mangal ◽  
C. M. Chandrashekar
Keyword(s):  
Discrete Time ◽  
Quantum Walk ◽  
Time Quantum ◽  
Walk Algorithm

scholarly journals Quantum algorithms for subset finding

2005 ◽  
Vol 5 (7) ◽  
pp. 593-604
Author(s):  
A.M. Childs ◽  
J.M. Eisenberg
Keyword(s):  
Lower Bounds ◽  
Discrete Time ◽  
Continuous Time ◽  
Quantum Algorithms ◽  
Quantum Walk ◽  
Query Complexity ◽  
Open Problems ◽  
Time Quantum ◽  
Query Algorithm ◽  
Walk Algorithm

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.

scholarly journals Quantum search on Hanoi network

2019 ◽  
Vol 17 (07) ◽  
pp. 1950060
Author(s):  
Pulak Ranjan Giri ◽  
Vladimir Korepin
Keyword(s):  
Quantum Walk ◽  
Quantum Walks ◽  
Periodic Lattice ◽  
Quantum Search ◽  
Main Structure ◽  
Running Time ◽  
One Dimensional ◽  
Target State ◽  
Amplitude Amplification ◽  
Walk Algorithm

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.

scholarly journals Quantum-walk-based search algorithms with multiple marked vertices

2021 ◽  
Vol 103 (6) ◽  
Author(s):  
G. A. Bezerra ◽  
P. H. G. Lugão ◽  
R. Portugal
Keyword(s):  
Quantum Walk ◽  
Search Algorithms

scholarly journals Bloch–Landau–Zener dynamics induced by a synthetic field in a photonic quantum walk

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