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Engineering Functional Quantum Algorithms

Andreas Klappenecker·Martin Roetteler
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Abstract

Suppose that a quantum circuit with K elementary gates is known for a unitary matrix U, and assume that U^m is a scalar matrix for some positive integer m. We show that a function of U can be realized on a quantum computer with at most O(mK+m^2log m) elementary gates. The functions of U are realized by a generic quantum circuit, which has a particularly simple structure. Among other results, we obtain efficient circuits for the fractional Fourier transform.

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Andreas Klappenecker, Martin Roetteler. 2002-08-20. Engineering Functional Quantum Algorithms. https://doi.org/10.1103/physreva.67.010302

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