Engineering Functional Quantum Algorithms
<|reference_start|>Engineering Functional Quantum Algorithms: 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.<|reference_end|>
@article{klappenecker2002engineering,
    title={Engineering Functional Quantum Algorithms},
    author={Andreas Klappenecker (Texas A&M University) and Martin Roetteler
  (Universitaet Karlsruhe)},
    journal={Physical Review A, 67, 010302, 2003},
    year={2002},
    doi={10.1103/PhysRevA.67.010302},
    archivePrefix={arXiv},
    eprint={quant-ph/0208130},
    primaryClass={quant-ph cs.ET}
}