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arXiv · 1512.07240

The block-ZXZ synthesis of an arbitrary quantum circuit

Alexis De Vos·Stijn De Baerdemacker
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Abstract

Given an arbitrary $2^w \times 2^w$ unitary matrix $U$, a powerful matrix decomposition can be applied, leading to four different syntheses of a $w$-qubit quantum circuit performing the unitary transformation. The demonstration is based on a recent theorem by Führ and Rzeszotnik, generalizing the scaling of single-bit unitary gates ($w=1$) to gates with arbitrary value of~$w$. The synthesized circuit consists of controlled 1-qubit gates, such as NEGATOR gates and PHASOR gates. Interestingly, the approach reduces to a known synthesis method for classical logic circuits consisting of controlled NOT gates, in the case that $U$ is a permutation matrix.

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Alexis De Vos, Stijn De Baerdemacker. 2016-11-17. The block-ZXZ synthesis of an arbitrary quantum circuit. https://doi.org/10.1103/physreva.94.052317

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