An Algorithmic Argument for Nonadaptive Query Complexity Lower Bounds on Advised Quantum Computation
Abstract
This paper employs a powerful argument, called an algorithmic argument, to prove lower bounds of the quantum query complexity of a multiple-block ordered search problem in which, given a block number i, we are to find a location of a target keyword in an ordered list of the i-th block. Apart from much studied polynomial and adversary methods for quantum query complexity lower bounds, our argument shows that the multiple-block ordered search needs a large number of nonadaptive oracle queries on a black-box model of quantum computation that is also supplemented with advice. Our argument is also applied to the notions of computational complexity theory: quantum truth-table reducibility and quantum truth-table autoreducibility.
Cite
@article{arxiv.quant-ph/0312003,
title = {An Algorithmic Argument for Nonadaptive Query Complexity Lower Bounds on Advised Quantum Computation},
author = {Harumichi Nishimura and Tomoyuki Yamakami},
journal= {arXiv preprint arXiv:quant-ph/0312003},
year = {2016}
}
Comments
16 pages. An extended abstract will appear in the Proceedings of the 29th International Symposium on Mathematical Foundations of Computer Science, Lecture Notes in Computer Science, Springer-Verlag, Prague, August 22-27, 2004