Harmonic sequence state-preparation
Quantum Physics
2026-03-02 v1
Abstract
We demonstrate an efficient circuit to prepare a quantum state with amplitudes proportional to a harmonic sequence. We do this by first preparing a large quantum state with linearly related amplitudes and then applying a quantum Fourier transform; this has a direct analogy to the fact that the Fourier coefficients of a sawtooth wave follow a harmonic sequence. We then consider an extension of this problem by block-encoding a matrix with a harmonic sequence along its diagonal. The cost of both circuits is dominated by the costs associated with the quantum Fourier transform.
Keywords
Cite
@article{arxiv.2602.23664,
title = {Harmonic sequence state-preparation},
author = {Benjamin Rempfer and Parker Kuklinski and Justin Elenewski and Kevin Obenland},
journal= {arXiv preprint arXiv:2602.23664},
year = {2026}
}