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arXiv · 1206.3223

A Depth-Optimal Canonical Form for Single-qubit Quantum Circuits

Alex Bocharov·Krysta M. Svore
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Abstract

Given an arbitrary single-qubit operation, an important task is to efficiently decompose this operation into an (exact or approximate) sequence of fault-tolerant quantum operations. We derive a depth-optimal canonical form for single-qubit quantum circuits, and the corresponding rules for exactly reducing an arbitrary single-qubit circuit to this canonical form. We focus on the single-qubit universal H,T basis due to its role in fault-tolerant quantum computing, and show how our formalism might be extended to other universal bases. We then extend our canonical representation to the family of Solovay-Kitaev decomposition algorithms, in order to find an ε-approximation to the single-qubit circuit in polylogarithmic time. For a given single-qubit operation, we find significantly lower-depth ε-approximation circuits than previous state-of-the-art implementations. In addition, the implementation of our algorithm requires significantly fewer resources, in terms of computation memory, than previous approaches.

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Alex Bocharov, Krysta M. Svore. 2012-06-14. A Depth-Optimal Canonical Form for Single-qubit Quantum Circuits. https://doi.org/10.1103/physrevlett.109.190501

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