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Probabilistic Cloning: Difference between revisions
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##'''Else''' the protocol failed and the final state of the machine is <math>|\Phi\rangle_{xy}</math> | ##'''Else''' the protocol failed and the final state of the machine is <math>|\Phi\rangle_{xy}</math> | ||
===The quantum circuit=== | |||
Finally, the quantum circuit which illustrates the above stages | Finally, the quantum circuit which illustrates the above stages can be described to consist of following gates and parts which have been also shown in the figure in [[Probabilistic Cloning#Outline|Outline]] | ||
* Reverse Controlled | * Reverse Controlled <math>U_1</math> gate: A controlled unitary gates with the <math>x</math> (original) qubit as the control qubit and the <math>z</math> qubit as the operational qubit. The unitary gate <math>U_1</math> acts only if the control qubit is <math>|0\rangle</math>. The unitary <math>U_1</math> is:</br> | ||
<math>U_1 = sin\beta |0\rangle\langle 0| + cos\beta |1\rangle\langle 0| + cos\beta |1\rangle\langle 0| - sin\beta |1\rangle\langle 1|</math></br> | <math>U_1 = sin\beta |0\rangle\langle 0| + cos\beta |1\rangle\langle 0| + cos\beta |1\rangle\langle 0| - sin\beta |1\rangle\langle 1|</math></br> | ||
where the <math>\beta = arcsin(\sqrt{\frac{1+tan^4\eta}{2}})</math> | where the <math>\beta = arcsin(\sqrt{\frac{1+tan^4\eta}{2}})</math> | ||