Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
A framework for fast quantum mechanical algorithms
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
The quantum query complexity of approximating the median and related statistics
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Multidimensional binary search trees used for associative searching
Communications of the ACM
Sublinear time approximate clustering
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Machine Learning
Machine Learning
Quantum Speed-Up of Markov Chain Based Algorithms
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
A hybrid classical-quantum clustering algorithm based on quantum walks
Quantum Information Processing
Quantum speed-up for unsupervised learning
Machine Learning
Histogram-based segmentation of quantum images
Theoretical Computer Science
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By the term "quantization", we refer to the process of using quantum mechanics in order to improve a classical algorithm, usually by making it go faster. In this paper, we initiate the idea of quantizing clustering algorithms by using variations on a celebrated quantum algorithm due to Grover. After having introduced this novel approach to unsupervised learning, we illustrate it with a quantized version of three standard algorithms: divisive clustering, k-medians and an algorithm for the construction of a neighbourhood graph. We obtain a significant speedup compared to the classical approach.