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arXiv · 2602.23664

Harmonic sequence state-preparation

Benjamin Rempfer·Parker Kuklinski·Justin Elenewski·Kevin Obenland
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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.

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Benjamin Rempfer, Parker Kuklinski, Justin Elenewski, Kevin Obenland. 2026-02-27. Harmonic sequence state-preparation. https://arxiv.org/abs/2602.23664

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