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Probabilistic Cloning: Difference between revisions
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'''The quantum circuit''' | '''The quantum circuit''' | ||
Finally, the quantum circuit which illustrates the above stages consists of following gates and parts which have been also shown in the figure in [[Probabilistic Cloning#Outline|Outline]] | Finally, the quantum circuit which illustrates the above stages consists of following gates and parts which have been also shown in the figure in [[Probabilistic Cloning#Outline|Outline]] | ||
* Reverse Controlled $U_1$ 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> | * Reverse Controlled $U_1$ 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> | |||
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> | ||
* A normal [[CNOT]] gate: The control qubit is <math>y</math> and the operational qubit is <math>x</math> (The flip occurs if the control qubit is <math>|1\rangle</math>) | * A normal [[CNOT]] gate: The control qubit is <math>y</math> and the operational qubit is <math>x</math> (The flip occurs if the control qubit is <math>|1\rangle</math>) | ||
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<math>U_2 = sin\delta |0\rangle\langle 0| + cos\delta |1\rangle\langle 0| + cos\delta |1\rangle\langle 0| - sin\delta |1\rangle\langle 1|</math></br> | <math>U_2 = sin\delta |0\rangle\langle 0| + cos\delta |1\rangle\langle 0| + cos\delta |1\rangle\langle 0| - sin\delta |1\rangle\langle 1|</math></br> | ||
where the <math>\delta = arcsin[(\sqrt{\frac{2}{1+tan^4\eta}} + \sqrt{\frac{2}{1+tan^{-4}\eta}})/2]</math> | where the <math>\delta = arcsin[(\sqrt{\frac{2}{1+tan^4\eta}} + \sqrt{\frac{2}{1+tan^{-4}\eta}})/2]</math> | ||
* [[Hadamard gate: A Hadamard gate on qubit | * [[Hadamard gate]]: A Hadamard gate on qubit <math>y</math> | ||
* Measurement part: Measuring qubit <math>z</math> in the standard basis. | * Measurement part: Measuring qubit <math>z</math> in the standard basis. | ||
==Further Information== | ==Further Information== | ||