The Solovay-Kitaev algorithm

Dawson, C.M., Nielsen, M.A. · 2006 · Quantum Information and Computation

| 编号 NA092 | 主题 线路综合与等价验证 | DOI 10.26421/qic6.1-6 |

摘要

摘要保留原文（英文）

摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。

2006 · Quantum Information and Computation This pedagogical review presents the proof of the Solovay-Kitaev theorem in the form of an efficient classical algorithm for compiling an arbitrary single-qubit gate into a sequence of gates from a fixed and finite set. The algorithm can be used, for example, to compile Shor’s algorithm, which uses rotations of $\pi /2^k$, into an efficient fault-tolerant form using only Hadamard, controlled-{\sc not}, and $\pi /8$ gates. The algorithm runs in $O({\log }^{2.71}(1/ϵ))$ time, and produces as output a sequence of $O({\log }^{3.97}(1/ϵ))$ quantum gates which is guaranteed to approximate the desired quantum gate to an accuracy within $ϵ>0$. We also explain how the algorithm can be generalized to apply to multi-qubit gates and to gates from $SU(d)$.

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