scholarly journals Time–space complexity of quantum search algorithms in symmetric cryptanalysis: applying to AES and SHA-2

2018 ◽  
Vol 17 (12) ◽  
Author(s):  
Panjin Kim ◽  
Daewan Han ◽  
Kyung Chul Jeong
Keyword(s):  
Search Algorithms ◽  
Space Complexity ◽  
Quantum Search ◽  
Time Space ◽  
Quantum Search Algorithms

scholarly journals Implementation of efficient quantum search algorithms on NISQ computers

2021 ◽  
Vol 20 (7) ◽  
Author(s):  
Kun Zhang ◽  
Pooja Rao ◽  
Kwangmin Yu ◽  
Hyunkyung Lim ◽  
Vladimir Korepin
Keyword(s):  
Search Algorithms ◽  
Quantum Search ◽  
Quantum Search Algorithms

How significant are the known collision and element distinctness quantum algorithms?

2004 ◽  
Vol 4 (3) ◽  
pp. 201-206
Author(s):  
L. Grover ◽  
T. Rudolph
Keyword(s):  
Search Algorithm ◽  
Quantum Algorithms ◽  
Search Space ◽  
Space Complexity ◽  
Quantum Search ◽  
Quantum Search Algorithm ◽  
Time Space ◽  
Simple Quantum ◽  
Structured Problems ◽  
Better Than

Quantum search is a technique for searching $N$ possibilities for a desired target in $O(\sqrt{N})$ steps. It has been applied in the design of quantum algorithms for several structured problems. Many of these algorithms require significant amount of quantum hardware. In this paper we propose the criterion that an algorithm which requires $O(S)$ hardware should be considered significant if it produces a speedup of better than $O\left(\sqrt{S}\right)$ over a simple quantum search algorithm. This is because a speedup of $O\left(\sqrt{S}\right)$ can be trivially obtained by dividing the search space into $S$ separate parts and handing the problem to $S$ independent processors that do a quantum search (in this paper we drop all logarithmic factors when discussing time/space complexity). Known algorithms for collision and element distinctness exactly saturate the criterion.

scholarly journals Quantum Search Algorithms for Wireless Communications

2019 ◽  
Vol 21 (2) ◽  
pp. 1209-1242 ◽  
Author(s):  
Panagiotis Botsinis ◽  
Dimitrios Alanis ◽  
Zunaira Babar ◽  
Hung Viet Nguyen ◽  
Daryus Chandra ◽  
...  
Keyword(s):  
Wireless Communications ◽  
Search Algorithms ◽  
Quantum Search ◽  
Quantum Search Algorithms

Phase Transitions for Quantum Search Algorithms

2005 ◽  
Author(s):  
Tad Hogg
Keyword(s):  
Phase Transitions ◽  
Computational Cost ◽  
Search Space ◽  
Search Algorithms ◽  
Quantum Search ◽  
Combinatorial Search ◽  
Problem Structure ◽  
Search Problems ◽  
Quantum Search Algorithms ◽  
The Many

Phase transitions have long been studied empirically in various combinatorial searches and theoretically in simplified models [91, 264, 301, 490]. The analogy with statistical physics [397], explored throughout this volume, shows how the many local choices made during search relate to global properties such as the resulting search cost. These studies have led to a better understanding of typical search behaviors [514] and improved search methods [195, 247, 261, 432, 433]. Among the current research questions in this field are the range of algorithms exhibiting the transition behavior and the algorithm-independent problem properties associated with the difficult instances concentrated near the transition. Towards this end, the present chapter examines quantum computer [123, 126, 158, 486] algorithms for nondeterministic polynomial (NP) combinatorial search problems [191]. As with many conventional methods, they exhibit the easy-hard-easy pattern of computational cost as the degree of constraint in the problems varies. We describe how properties of the search space affect the algorithms and identify an additional structural property, the energy gap, motivated by one quantum algorithm but applicable to a variety of techniques, both quantum and classical. Thus, the study of quantum search algorithms not only extends the range of algorithms exhibiting phase transitions, but also helps identify underlying structural properties. Specifically, the next two sections describe a class of hard search problems and the form of quantum search algorithms proposed to date. The remainder of the chapter presents algorithm behaviors, relevant problem structure, arid an approximate asymptotic analysis of their cost scaling. The final section discusses various open issues in designing and evaluating quantum algorithms, and relating their behavior to problem structure. The k-satisfiability (k -SAT) problem, as discussed earlier in this volume, consists of n Boolean variables and m clauses. A clause is a logical OR of k variables, each of which may be negated. A solution is an assignment, that is, a value for each variable, TRUE or FALSE, satisfying all the clauses. An assignment is said to conflict with any clause it does not satisfy.

scholarly journals Quantum search algorithms on the hypercube

2009 ◽  
Vol 42 (8) ◽  
pp. 085303 ◽  
Author(s):  
Birgit Hein ◽  
Gregor Tanner
Keyword(s):  
Search Algorithms ◽  
Quantum Search ◽  
Quantum Search Algorithms

scholarly journals Quantum search algorithms on hierarchical networks

2011 ◽  
Author(s):  
Franklin de Lima Marquezino ◽  
Renato Portugal ◽  
Stefan Boettcher
Keyword(s):  
Search Algorithms ◽  
Quantum Search ◽  
Hierarchical Networks ◽  
Quantum Search Algorithms

scholarly journals Models of quantum search algorithms. Introduction for IT students –pedagogical examples

2020 ◽  
pp. 126-151
Author(s):  
Olga Ivancova ◽  
Nikita Ryabov ◽  
Vladimir Korenkov ◽  
Sergey Ulyanov
Keyword(s):  
Computational Algorithm ◽  
Quantum Algorithms ◽  
Search Algorithms ◽  
Quantum Search ◽  
Search Problems ◽  
Quantum Oracle ◽  
Quantum Search Algorithms

This article is one of a series of articles on quantum algorithms. The article discusses quantum oracle models and Grover's computational algorithm for search problems in an unstructured database.

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