Learning-Graph-Based Quantum Algorithm for k-Distinctness
Aleksandrs Belovs
- pp 207-216
TLDR
In this paper, a quantum algorithm for the k-distinctness problem is presented, which solves the problem in a less number of queries than the previous algorithm by Ambainis.Abstract:
We present a quantum algorithm solving the k-distinctness problem in a less number of queries than the previous algorithm by Ambainis. The construction uses a modified learning graph approach. Compared to the recent paper by Belovs and Lee, the algorithm doesn't require any prior information on the input, and the complexity analysis is much simpler.read more
Citations
More filters
Proceedings ArticleDOI
The polynomial method strikes back: tight quantum query bounds via dual polynomials
TL;DR: For any constant k, the quantum query complexity of the k-distinctness function is Ω(n3/4−1/(2k+2−4) as discussed by the authors.
Proceedings Article
Approximating edit distance in truly subquadratic time: quantum and mapreduce
TL;DR: In this article, a MapReduce algorithm was proposed to approximate the edit distance within a factor of 3, with sublinearly many machines and sublinear memory, in a logarithmic number of rounds.
Book ChapterDOI
Span programs and quantum algorithms for st -connectivity and claw detection
TL;DR: An algorithm is given that uses O(n) queries to the adjacency matrix of an n-vertex graph to decide if vertices s and t are connected, under the promise that they either are connected by a path of length at most d, or are disconnected.
Book ChapterDOI
Time-Efficient quantum walks for 3-distinctness
TL;DR: Two quantum walk algorithms for 3-Distinctness are presented, improving the previous $\tilde{O}(n^{3/4})$ and matching the best known upper bound for query complexity (obtained via learning graphs) up to log factors.
Journal ArticleDOI
Quantum Algorithm Design: Techniques and Applications
Changpeng Shao,Yang Li,Hongbo Li +2 more
TL;DR: An overview of the development of quantum algorithms, then five important techniques are investigated: Quantum phase estimation, linear combination of unitaries, quantum linear solver, Grover search, and quantum walk, together with their applications in quantum state preparation, quantum machine learning, and Quantum search.
References
More filters
Journal ArticleDOI
Tight bounds on quantum searching
TL;DR: A lower bound on the efficiency of any possible quantum database searching algorithm is provided and it is shown that Grover''s algorithm nearly comes within a factor 2 of being optimal in terms of the number of probes required in the table.
Journal ArticleDOI
Complexity measures and decision tree complexity: a survey
Harry Buhrman,Ronald de Wolf +1 more
TL;DR: Several complexity measures for Boolean functions are discussed: certificate complexity, sensitivity, block sensitivity, and the degree of a representing or approximating polynomial, and how they give bounds for the decision tree complexity of Boolean functions on deterministic, randomized, and quantum computers.
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
Tight bounds on quantum searching
TL;DR: In this article, a tight analysis of Grover's recent algorithm for quantum database searching is provided, where the probability of success after any given number of iterations of the algorithm is given.
Journal ArticleDOI
Quantum Walk Algorithm for Element Distinctness
TL;DR: 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.