Work

A Strong Direct Product Theorem for Quantum Query Complexity

Year: 2012

Type: conference-paper

Abstract: We show that quantum query complexity satisfies a strong direct product theorem. This means that computing $k$ copies of a function with less than $k$ times the quantum queries needed to compute one copy of the function implies that the overall success probability will be exponentially small in $k$. For a boolean function $f$ we also show an XOR lemma -- computing the parity of $k$ copies of $f$ with less than $k$ times the queries needed for one copy implies that the advantage over random guessing will be exponentially small. We do this by showing that the multiplicative adversary method, which inherently satisfies a strong direct product theorem, characterizes bounded-error quantum query complexity. In particular, we show that the multiplicative adversary bound is always at least as large as the additive adversary bound, which is known to characterize bounded-error quantum query complexity.

Source: Proceedings - IEEE Conference on Computational Complexity/Proceedings

DOI: 10.1109/ccc.2012.17

Authors: Troy Lee, Jeremie Roland

Institution: Université Libre de Bruxelles

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Strong, Army Research Office

Awards: G4511331183, G7452299184