# Topological obstructions to implementing quantum if-clause

@inproceedings{Gavorova2020TopologicalOT, title={Topological obstructions to implementing quantum if-clause}, author={Zuzana Gavorov'a and Matan Seidel and Yonathan Touati}, year={2020} }

Some tasks are impossible in a quantum circuit, even though their classical versions are easy in a classical circuit. An example with far-reaching consequences is cloning [1]. Another task commonly used in classical computation is the if-clause. Its quantum version applies an unknown n -qubit unitary U P U p 2 n q if and only if a control qubit is 1. We identify it with control φ p U q “ | 0 (cid:105)(cid:104) 0 |b I ` e iφ p U q | 1 (cid:105)(cid:104) 1 |b U , for any real function φ . It was…

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