Approximate Quantum Fourier Transform in Logarithmic Depth on a Line
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910921845112832 |
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| author | Bäumer, Elisa Sutter, David Woerner, Stefan |
| author_facet | Bäumer, Elisa Sutter, David Woerner, Stefan |
| contents | The approximate quantum Fourier transform (AQFT) on $n$ qubits can be implemented in logarithmic depth using $8n$ qubits with all-to-all connectivity, as shown in [Hales, PhD Thesis Berkeley, 2002]. However, realizing the required all-to-all connectivity can be challenging in practice. In this work, we use dynamic circuits, i.e., mid-circuit measurements and feed-forward operations, to implement the AQFT in logarithmic depth using only $4n$ qubits arranged on a line with nearest-neighbor connectivity. Furthermore, for states with a specific structure, the number of qubits can be further reduced to $2n$ while keeping the logarithmic depth and line connectivity. As part of our construction, we introduce a new implementation of an adder with logarithmic depth on a line, which allows us to improve the AQFT construction of Hales. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20832 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximate Quantum Fourier Transform in Logarithmic Depth on a Line Bäumer, Elisa Sutter, David Woerner, Stefan Quantum Physics The approximate quantum Fourier transform (AQFT) on $n$ qubits can be implemented in logarithmic depth using $8n$ qubits with all-to-all connectivity, as shown in [Hales, PhD Thesis Berkeley, 2002]. However, realizing the required all-to-all connectivity can be challenging in practice. In this work, we use dynamic circuits, i.e., mid-circuit measurements and feed-forward operations, to implement the AQFT in logarithmic depth using only $4n$ qubits arranged on a line with nearest-neighbor connectivity. Furthermore, for states with a specific structure, the number of qubits can be further reduced to $2n$ while keeping the logarithmic depth and line connectivity. As part of our construction, we introduce a new implementation of an adder with logarithmic depth on a line, which allows us to improve the AQFT construction of Hales. |
| title | Approximate Quantum Fourier Transform in Logarithmic Depth on a Line |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2504.20832 |