Harmonic sequence state-preparation
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910034847334400 |
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| author | Rempfer, Benjamin Kuklinski, Parker Elenewski, Justin Obenland, Kevin |
| author_facet | Rempfer, Benjamin Kuklinski, Parker Elenewski, Justin Obenland, Kevin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23664 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Harmonic sequence state-preparation Rempfer, Benjamin Kuklinski, Parker Elenewski, Justin Obenland, Kevin Quantum Physics 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. |
| title | Harmonic sequence state-preparation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2602.23664 |