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arXiv · 2610.32693

Elementary proofs of quantum lower bounds for element distinctness and k-sum

Andris Ambainis·Martins Kokainis
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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.

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Andris Ambainis, Martins Kokainis. 2026-10-23. Elementary proofs of quantum lower bounds for element distinctness and k-sum. https://arxiv.org/abs/2610.32693

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