Quantum algorithms for subset finding

@article{Childs2005QuantumAF,
  title={Quantum algorithms for subset finding},
  author={Andrew M. Childs and Jason M. Eisenberg},
  journal={Quantum Inf. Comput.},
  year={2005},
  volume={5},
  pages={593-604}
}
Recently, Ambainis gave an O(N2/3)-query discrete-time quantum walk algorithm forthe element distinctness problem, and more generally, an O(NL/(L+1))-query algorithmfor finding L equal numbers. We review this algorithm and give a simplified and tightenedanalysis of its query complexity using techniques previously applied to the analysis ofcontinuous-time quantum walk. We also briefly discuss applications of the algorithm andpose two open problenm regarding continuous-time quantum walk and lower… 
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75 Citations
Highly Influential Citations
4
Background Citations
21
Methods Citations
19

75 Citations

Quantum walk algorithm for element distinctness
  • A. Ambainis
  • Computer Science
    45th Annual IEEE Symposium on Foundations of Computer Science
  • 2004
TLDR
An O(N/sup k/(k+1)/) query quantum algorithm is given for the generalization of element distinctness in which the authors have to find k equal items among N items.
An Improved Claw Finding Algorithm Using Quantum Walk
  • S. Tani
  • Mathematics, Computer Science
    MFCS
  • 2007
TLDR
A quantum-walk-based algorithm is described that can be generalized to find a claw of k functions for any constant integer k > 1, where the domains of the functions may have different size.
Learning-Graph-Based Quantum Algorithm for k-Distinctness
  • Aleksandrs Belovs
  • Computer Science
    2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
  • 2012
TLDR
A quantum algorithm solving the k-distinctness problem in a less number of queries than the previous algorithm by Ambainis is presented, and the complexity analysis is much simpler.
Applications of Adversary Method in Quantum Query Algorithms
TLDR
A recently developed tight characterisation of quantum query complexity, the adversary bound, is used to develop new quantum algorithms and lower bounds, and a generalisation ofquantum walks that connects electrical properties of a graph and its quantum hitting time is developed.
Promised and Distributed Quantum Search
TLDR
A tight bound of the quantum query complexity for the Claw Finding problem is shown, improving previous upper and lower bounds by Buhrman, Durr, Heiligman, Hoyer, Magniez, Santha and de Wolf.
Claw finding algorithms using quantum walk
  • S. Tani
  • Computer Science, Mathematics
    Theor. Comput. Sci.
  • 2009
A Quantum Approach to Subset-Sum and Similar Problems
TLDR
This paper studies the subset-sum problem by using a quantum heuristic approach similar to the verification circuit of quantum Arthur-Merlin games and shows that the exact solution of the subset sum problem my be obtained in polynomial time and the exponential speed up over the classical algorithms may be possible.
Quantum Walks and Electric Networks
We prove that a quantum walk can detect the presence of a marked element in a graph in $O(\sqrt{WR})$ steps for any initial probability distribution on vertices. Here, $W$ is the total weight of the…
Improved Quantum Information Set Decoding
TLDR
This paper gives an alternative view on the quantum walk based algorithms proposed by Kachigar and Tillich (PQCrypto'17) and translates May-Ozerov Near Neighbour technique (Eurocrypt'15) to an `update-and-query' language more suitable for the quantumWalk framework.
Quantum Algorithm for Commutativity Testing of a Matrix Set
TLDR
It turns out Szegedy's algorithm can be generalized to solve similar problems and is used to analyze the problem of matrix set commutativity, which is probably the first problem to be studied on the quantum query complexity using quantum walks that involves more than one parameter.
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