Catalytic $z$-rotations in constant $T$-depth Article Swipe

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Isaac H. Kim ·

YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2506.15147

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 $\log (1/ε)$.

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2506.15147
PDF: https://arxiv.org/pdf/2506.15147
OA Status: green
OpenAlex ID: https://openalex.org/W4415333506

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DOI: https://doi.org/10.48550/arxiv.2506.15147

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Title: Catalytic $z$-rotations in constant $T$-depth

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Type: preprint

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Language: en

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Publication year: 2025

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Publication date: 2025-06-18

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Authors: Isaac H. Kim

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Landing page: https://arxiv.org/abs/2506.15147

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PDF URL: https://arxiv.org/pdf/2506.15147

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