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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2506.15147 |
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| _version_ | 1866910020352868352 |
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| author | Kim, Isaac H. |
| author_facet | Kim, Isaac H. |
| contents | We show that the $T$-depth of any single-qubit $z$-rotation can be reduced to $3$ if a certain catalyst state is available. To achieve an $ε$-approximation, it suffices to have a catalyst state of size polynomial in $\log(1/ε)$. This implies that $\mathsf{QNC}^0_f/\mathsf{qpoly}$ admits a finite universal gate set consisting of Clifford+$T$. In particular, there are catalytic constant $T$-depth circuits that approximate multi-qubit Toffoli, adder, and quantum Fourier transform arbitrarily well. We also show that the catalyst state can be prepared in time polynomial in $\log (1/ε)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15147 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Catalytic $z$-rotations in constant $T$-depth Kim, Isaac H. Quantum Physics We show that the $T$-depth of any single-qubit $z$-rotation can be reduced to $3$ if a certain catalyst state is available. To achieve an $ε$-approximation, it suffices to have a catalyst state of size polynomial in $\log(1/ε)$. This implies that $\mathsf{QNC}^0_f/\mathsf{qpoly}$ admits a finite universal gate set consisting of Clifford+$T$. In particular, there are catalytic constant $T$-depth circuits that approximate multi-qubit Toffoli, adder, and quantum Fourier transform arbitrarily well. We also show that the catalyst state can be prepared in time polynomial in $\log (1/ε)$. |
| title | Catalytic $z$-rotations in constant $T$-depth |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2506.15147 |