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Quantum search algorithms
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A review of quantum algorithms for search problems can be found in this paper, where Grover's search algorithm, its generalization to amplitude amplification, the applications of amplitude amplification to various problems and the recent quantum algorithms based on quantum walks.Abstract:
We review some of quantum algorithms for search problems: Grover's search algorithm, its generalization to amplitude amplification, the applications of amplitude amplification to various problems and the recent quantum algorithms based on quantum walks.read more
Citations
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Journal ArticleDOI
Quantum walks: a comprehensive review
TL;DR: This paper has reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.
Proceedings ArticleDOI
Quantum speed-up of Markov chain based algorithms
TL;DR: In this paper, a generic method for quantizing classical algorithms based on random walks was developed, and it was shown that under certain conditions, the quantum version gives rise to a quadratic speedup.
Journal ArticleDOI
Efficient distributed quantum computing
Robert Beals,Stephen Brierley,Oliver Gray,Aram W. Harrow,Samuel Kutin,Noah Linden,Dan J. Shepherd,Mark Stather +7 more
TL;DR: A parallel quantum search algorithm is presented that can be used by algorithm designers without worrying whether the underlying architecture supports the connectivity of the circuit and improves the time–space trade-off for the element distinctness and collision finding problems.
Book
Quantum Walks for Computer Scientists
TL;DR: The purpose of this lecture is to provide a concise yet comprehensive introduction to quantum walks, an emerging field of quantum computation, is a generalization of random walks into the quantum mechanical world.
Journal ArticleDOI
Optimized quantum random-walk search algorithms on the hypercube
TL;DR: Improvements to the SKW algorithm are presented which yield a significant increase in success probability, and an improvement on query complexity such that the theoretical limit of a search algorithm succeeding with probability close to one is reached.
References
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Journal ArticleDOI
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
TL;DR: In this paper, the authors considered factoring integers and finding discrete logarithms on a quantum computer and gave an efficient randomized algorithm for these two problems, which takes a number of steps polynomial in the input size of the integer to be factored.
Proceedings ArticleDOI
A fast quantum mechanical algorithm for database search
TL;DR: In this paper, it was shown that a quantum mechanical computer can solve integer factorization problem in a finite power of O(log n) time, where n is the number of elements in a given integer.
Journal ArticleDOI
A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
TL;DR: For the small examples that the authors could simulate, the quantum adiabatic algorithm worked well, providing evidence that quantum computers (if large ones can be built) may be able to outperform ordinary computers on hard sets of instances of NP-complete problems.
Journal ArticleDOI
Quantum random walks: an introductory overview
TL;DR: This article will introduce quantum random walks, review some of their properties and outline their striking differences to classical walks, introducing some of the main concepts and language of present day quantum information science in this context.
OtherDOI
Quantum Amplitude Amplification and Estimation
TL;DR: In this article, the amplitude amplification algorithm was proposed to find a good solution after an expected number of applications of the algorithm and its inverse which is proportional to a factor proportional to 1/a.