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arXiv · 2112.02040

Efficient Universal Quantum Compilation: An Inverse-free Solovay-Kitaev Algorithm

Adam Bouland·Tudor Giurgica-Tiron
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Abstract

The Solovay-Kitaev algorithm is a fundamental result in quantum computation. It gives an algorithm for efficiently compiling arbitrary unitaries using universal gate sets: any unitary can be approximated by short gates sequences, whose length scales merely poly-logarithmically with accuracy. As a consequence, the choice of gate set is typically unimportant in quantum computing. However, the Solovay-Kitaev algorithm requires the gate set to be inverse-closed. It has been a longstanding open question if efficient algorithmic compilation is possible without this condition. In this work, we provide the first inverse-free Solovay-Kitaev algorithm, which makes no assumption on the structure within a gate set beyond universality, answering this problem in the affirmative, and providing an efficient compilation algorithm in the absence of inverses for both $\text{SU}(d)$ and $\text{SL}(d, \mathbb{C})$. The algorithm works by showing that approximate gate implementations of the generalized Pauli group can self-correct their errors.

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Adam Bouland, Tudor Giurgica-Tiron. 2021-12-03. Efficient Universal Quantum Compilation: An Inverse-free Solovay-Kitaev Algorithm. https://arxiv.org/abs/2112.02040

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