On Randomized and Quantum Query Complexities

Details On Randomized and Quantum Query Complexities On Randomized and Quantum Query Complexities

2005-01-25

arxiv.org/abs/quant-ph/0501142v3

Physics

Quantum Physics

10 pages

Scientific paper

We study randomized and quantum query (a.k.a. decision tree) complexity for all total Boolean functions, with emphasis to derandomization and dequantization (removing quantumness from algorithms). Firstly, we show that $D(f) = O(Q_1(f)^3)$ for any total function $f$, where $D(f)$ is the minimal number of queries made by a deterministic query algorithm and $Q_1(f)$ is the number of queries made by any quantum query algorithm (decision tree analog in quantum case) with one-sided constant error; both algorithms compute function $f$. Secondly, we show that for all total Boolean functions $f$ holds $R_0(f)=O(R_2(f)^2 \log N)$, where $R_0(f)$ and $R_2(f)$ are randomized zero-sided (a.k.a Las Vegas) and two-sided (a.k.a. Monte Carlo) error query complexities.

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