Year: 2026
Type: preprint
Abstract: We give elementary proofs of the $Ω(n^{2/3})$ quantum query lower bound for element distinctness and the $Ω(n^{k/(k+1)})$ lower bound for the $k$-sum problem, for fixed $k$ and sufficiently large groups. The proofs use only basic properties of quantum states and linear algebra, analyzing the differences of algorithm states on different inputs.
Source: arXiv (Cornell University)
Authors: Ambainis, Andris, Kokainis, Martins
Institution: University of Latvia
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223679833