On the Irresistible Efficiency of Signal Processing Methods in Quantum Computing

Details On the Irresistible Efficiency of Signal Processing Methods in Quantum Computing On the Irresistible Efficiency of Signal Processing Methods in Quantum Computing

2001-11-07

arxiv.org/abs/quant-ph/0111039v1

Physics

Quantum Physics

15 pages, LaTeX 2e. Expanded version of quant-ph/0111038. SPECLOG 2000, Tampere, Finland

Scientific paper

We show that many well-known signal transforms allow highly efficient realizations on a quantum computer. We explain some elementary quantum circuits and review the construction of the Quantum Fourier Transform. We derive quantum circuits for the Discrete Cosine and Sine Transforms, and for the Discrete Hartley transform. We show that at most O(log^2 N) elementary quantum gates are necessary to implement any of those transforms for input sequences of length N.

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