Optimization of the Solovay-Kitaev algorithm

Tien Trung Pham, Rodney Van Meter, Clare Horsman

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)


The Solovay-Kitaev algorithm is the standard method used for approximating arbitrary single-qubit gates for fault-tolerant quantum computation. In this paper we introduce a technique called search space expansion, which modifies the initial stage of the Solovay-Kitaev algorithm, increasing the length of the possible approximating sequences but without requiring an exhaustive search over all possible sequences. This technique is combined with an efficient space search method called geometric nearest-neighbor access trees, modified for the unitary matrix lookup problem, in order to reduce significantly the algorithm run time. We show that, with low time cost, our techniques output gate sequences that are almost an order of magnitude smaller for the same level of accuracy. This therefore reduces the error correction requirements for quantum algorithms on encoded fault-tolerant hardware.

Original languageEnglish
Article number052332
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number5
Publication statusPublished - 2013 May 30

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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