Learning-Graph-Based Quantum Algorithm for k-Distinctness

Aleksandrs Belovs
2012 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science  
We present a quantum algorithm solving the k-distinctness problem in O n 1−2 k−2 /(2 k −1) queries with a bounded error. This improves the previous O(n k/(k+1) )-query algorithm by Ambainis. The construction uses a modified learning graph approach. Compared to the recent paper by Belovs and Lee [6], the algorithm doesn't require any prior information on the input, and the complexity analysis is much simpler.
doi:10.1109/focs.2012.18 dblp:conf/focs/Belovs12 fatcat:o4gp5vtccbdgpmrofiwtmtlmrm