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Replacing Two Controlled-U's with Two CNOTs

Robert R. Tucci
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Abstract

We give a simple, closed-form formula, what we call the Deflation Identity, for converting any 2-qubit circuit with exactly two controlled-U's (and some 1-qubit rotations) into an equivalent circuit with just two CNOTs (and some 1-qubit rotations). We also give two interesting applications of the Deflation Identity; one to "opening and closing a breach" in a quantum circuit, the other to the CS decomposition of a 2-qubit operator.

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Robert R. Tucci. 2005-09-15. Replacing Two Controlled-U's with Two CNOTs. https://arxiv.org/abs/quant-ph/0509111

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