Quantum search algorithms

@article{Ambainis2004QuantumSA,
  title={Quantum search algorithms},
  author={A. Ambainis},
  journal={SIGACT News},
  year={2004},
  volume={35},
  pages={22-35}
}
  • A. Ambainis
  • Published 2004
  • Mathematics, Computer Science, Physics
  • SIGACT News
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. 
QUANTUM ALGORITHMS OF DECISION AND PLANNING PROBLEMS
We give an overview of quantum algorithms of some graph problems. We discuss the rate of speedup compared to the corresponding classical algorithms. Some possible applications in decision andExpand
Grover's Algorithm with Errors
Grover’s algorithm is a quantum search algorithm solving the unstructured search problem of size n in \(O(\sqrt{n})\) queries, while any classical algorithm needs O(n) queries [3].
Quantum Algorithms
  • M. Mosca
  • Computer Science, Physics
  • Encyclopedia of Complexity and Systems Science
  • 2009
TLDR
This work provides an explicit algorithm for generating any prescribed interference pattern with an arbitrary precision for quantum algorithms and shows how they are related to diierent instances of quantum phase estimation. Expand
Impossibility of a Quantum Speed-Up with a Faulty Oracle
We consider Grover's unstructured search problem in the setting where each oracle call has some small probability of failing. We show that no quantum speed-up is possible in this case.
Quantum algorithms for fixed points and invariant subgroups
TLDR
A quantum algorithm is applied to solve problems concerning fixed points and invariant subgroups of automorphisms by computes the intersection of multiple unsorted multisets whose elements originate from the same set. Expand
Grover's Search with Faults on Some Marked Elements
Grover’s algorithm is a quantum query algorithm solving the unstructured search problem of size N using O(N) queries. It provides a significant speed-up over any classical algorithm [3]. The runnin...
Quantum Complexity Bounds of Independent Set Problems
TLDR
This work gives quantum algorithms for computing a maximal and a maximum independent set in a graph and improves the best classical complexity bounds for the corresponding problems. Expand
Quantum Algorithms for Graph Problems A Survey
In this survey we give an overview about important methods to construct quantum algorithms and quantum lower bounds for graph problems. We show how to use these methods, and we give a summary aboutExpand
Efficient distributed quantum computing
  • R. Beals, S. Brierley, +5 authors M. Stather
  • Mathematics, Physics
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2013
We provide algorithms for efficiently moving and addressing quantum memory in parallel. These imply that the standard circuit model can be simulated with a low overhead by a more realistic model of aExpand
Quantum walks and ground state problems
Since the appearance of Shor's factoring algorithm in 1994, the search for novel quantum computer algorithms has proved surprisingly difficult. Two design approaches that have yielded some progressExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 38 REFERENCES
Quantum Counting
TLDR
This work generalizes the Grover iteration in the light of a concept called amplitude amplification, and shows that the quadratic speedup obtained by the quantum searching algorithm over classical brute force can still be obtained for a large family of search problems for which good classical heuristics exist. Expand
QUANTUM WALKS AND THEIR ALGORITHMIC APPLICATIONS
TLDR
An overview of quantum walks is given, with emphasis on their algorithmic applications, which are quantum counterparts of Markov chains. Expand
A framework for fast quantum mechanical algorithms
TLDR
The sqrt(N) step quantum search algorithm is an immediate consequence of a framework for the design and analysis of quantum mechanical algorithms, and several other search-type applications are presented. Expand
Quantum Algorithms for Element Distinctness
We present several applications of quantum amplitude amplification for deciding whether all elements in the image of a given function are distinct, for finding an intersection of two sorted tables,Expand
GROVER'S QUANTUM SEARCHING ALGORITHM IS OPTIMAL
I show that for any number of oracle lookups up to about {pi}/4thinsp{radical} (N) , Grover{close_quote}s quantum searching algorithm gives the maximal possible probability of finding the desiredExpand
Exact quantum query complexity for total Boolean functions
We will show that if there exists a quantum query algorithm that exactly computes some total Boolean function f by making T queries, then there is a classical deterministic algorithm A that exactlyExpand
A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
TLDR
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. Expand
Quantum algorithms for subset finding
TLDR
This algorithm is reviewed and a simplified and tightened analysis of its query complexity is given using techniques previously applied to the analysis of continuous-time quantum walk. Expand
Quantum random walks: An introductory overview
TLDR
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. Expand
How significant are the known collision and element distinctness quantum algorithms?
TLDR
The criterion that an algorithm width requires O(S) hardware to be considered significant if it produces a speedup of better than O(√S) over asimple quantum search algorithm is proposed. Expand
...
1
2
3
4
...