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

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 $\frac{1}{\epsilon }$, and expected gate depth also logarithmic in $\frac{1}{\epsilon }$.

6 pages, 3 figures, v4: close to published version

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Cited by in corpus (1)

• Practical implementation of Toffoli-based qubit rotation