The Quantum Query Complexity of Algebraic Properties

Sebastian Dörn and Thomas Thierauf

Abstract:
In this paper we present an application of the quantum walk search schema by Magniez et al. for finding more than one solution of a search problem. We apply our quantum walk to matrix multiplication, thereby improving a result by Buhrman and Spalek. Futhermore we give tight quantum query complexity bounds of some important linear algebra problems, like the determinant, rank, matrix inverse and the matrix power problem.

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