Quantum Fourier transform in computational basis

S. S. Zhou, T. Loke, J. A. Izaac, J. B. Wang

    Research output: Contribution to journalArticlepeer-review

    27 Citations (Scopus)

    Abstract

    The quantum Fourier transform, with exponential speed-up compared to the classical fast Fourier transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, Shor’s factoring algorithm). However, situations arise where it is not sufficient to encode the Fourier coefficients within the quantum amplitudes, for example in the implementation of control operations that depend on Fourier coefficients. In this paper, we detail a new quantum scheme to encode Fourier coefficients in the computational basis, with fidelity 1 - δ and digit accuracy ϵ for each Fourier coefficient. Its time complexity depends polynomially on log (N) , where N is the problem size, and linearly on 1 / δ and 1 / ϵ. We also discuss an application of potential practical importance, namely the simulation of circulant Hamiltonians.

    Original languageEnglish
    Article number82
    JournalQuantum Information Processing
    Volume16
    Issue number3
    DOIs
    Publication statusPublished - 1 Mar 2017

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