dorsal/arxiv
View SchemaOn Randomized and Quantum Query Complexities
| Authors | Gatis Midrijanis |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0501142 |
| URL | https://arxiv.org/abs/quant-ph/0501142 |
Abstract
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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"abstract": "We study randomized and quantum query (a.k.a. decision tree) complexity for\nall total Boolean functions, with emphasis to derandomization and\ndequantization (removing quantumness from algorithms). Firstly, we show that\n$D(f) = O(Q_1(f)^3)$ for any total function $f$, where $D(f)$ is the minimal\nnumber of queries made by a deterministic query algorithm and $Q_1(f)$ is the\nnumber of queries made by any quantum query algorithm (decision tree analog in\nquantum case) with one-sided constant error; both algorithms compute function\n$f$. Secondly, we show that for all total Boolean functions $f$ holds\n$R_0(f)=O(R_2(f)^2 \\log N)$, where $R_0(f)$ and $R_2(f)$ are randomized\nzero-sided (a.k.a Las Vegas) and two-sided (a.k.a. Monte Carlo) error query\ncomplexities.",
"arxiv_id": "quant-ph/0501142",
"authors": [
"Gatis Midrijanis"
],
"categories": [
"quant-ph"
],
"title": "On Randomized and Quantum Query Complexities",
"url": "https://arxiv.org/abs/quant-ph/0501142"
},
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