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 [18] that improves the previous bounds by Ambainis [3] and Szegedy [23]. We also present several lower bounds for testing algebraic properties.
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Dörn, S., Thierauf, T. (2007). The Quantum Query Complexity of Algebraic Properties. In: Csuhaj-Varjú, E., Ésik, Z. (eds) Fundamentals of Computation Theory. FCT 2007. Lecture Notes in Computer Science, vol 4639. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74240-1_22
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DOI: https://doi.org/10.1007/978-3-540-74240-1_22
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