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…
75 Citations
Quantum walk algorithm for element distinctness
- Computer Science45th Annual IEEE Symposium on Foundations of Computer Science
- 2004
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
- Mathematics, Computer ScienceMFCS
- 2007
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
- Computer Science2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
- 2012
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
- Computer Science, Mathematics
- 2014
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
- Computer ScienceCOCOON
- 2005
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.
A Quantum Approach to Subset-Sum and Similar Problems
- MathematicsArXiv
- 2017
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
- Mathematics
- 2013
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
- Computer SciencePQCrypto
- 2018
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
- Computer Science, Mathematics
- 2005
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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