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The Quantum Query Complexity of Algebraic Properties

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arxiv 0705.1446 v1 pith:NLFZC73J submitted 2007-05-10 quant-ph

classification quant-ph
keywords boundsquantumalgebraiccomplexitypropertiesquerytestingwhether
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abstract

We present quantum query complexity bounds for testing algebraic properties. For a set S and a binary operation on S, we consider the decision problem whether $S$ is a semigroup or has an identity element. If S is a monoid, we want to decide whether S is a group. We present quantum algorithms for these problems that improve the best known classical complexity bounds. In particular, we give the first application of the new quantum random walk technique by Magniez, Nayak, Roland, and Santha that improves the previous bounds by Ambainis and Szegedy. We also present several lower bounds for testing algebraic properties.

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Cited by 1 Pith paper

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  1. The Compressed Oracle is a Worthy (Multiplicative) Adversary

    quant-ph 2025-09 conditional novelty 6.0 of 10

    The compressed oracle technique is captured by the multiplicative adversary method through the new multiplicative ladder adversary method, up to a factor of 6.

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