Singlet states and the estimation of eigenstates and eigenvalues of an unknown Controlled-$U$ gate

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Authors	HILLERY Mark BŮŽEK Vladimír
Year of publication	2001
Type	Article in Periodical
Magazine / Source	Physical Review A
MU Faculty or unit	Faculty of Informatics
Citation
Field	Informatics
Keywords	QUANTUM
Description	We consider several problems that involve finding the eigenvalues and generating the eigenstates of unknown unitary gates. We first examine controlled-U gates that act on qubits and assume that we know the eigenvalues. It is then shown how to use singlet states to produce qubits in the eigenstates of the gate. We then remove the assumption that we know the eigenvalues and show how to both find the eigenvalues and produce qubits in the eigenstates. Finally. we look at the case where the unitary operation acts on qutrits and it has two eigenvalues of 1 and one of - 1. We are able to use a singlet state to produce a qutrit in the eigenstate corresponding to the - 1 eigenvalue.
Related projects:	Informatics as the third methodology Non-sequential Models of Computing -- Quantum and Concurrent Distributed Models of Computing