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arXiv · 2404.05618

Single-qubit rotation algorithm with logarithmic Toffoli count and gate depth

Christoffer Hindlycke·Jan-Åke Larsson
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Abstract

We propose a direct (non-recursive) algorithm for applying a rotation $R_{\theta^\ast}$, $\epsilon$-close to a desired rotation $R_\theta$, to a single qubit using the Clifford+Toffoli gate set. Our algorithm does not rely on repeatedly applying a fixed rotation, but immediately applies $R_{\theta^\ast}$. It succeeds with probability strictly greater than $1/2$, has an expected number of repetitions strictly less than 2, expected Toffoli count logarithmic in $\tfrac{1}{\epsilon}$, and expected gate depth also logarithmic in $\tfrac{1}{\epsilon}$.

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Christoffer Hindlycke, Jan-Åke Larsson. 2024-04-08. Single-qubit rotation algorithm with logarithmic Toffoli count and gate depth. https://doi.org/10.1103/physrevresearch.6.l042027

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