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Probabilistic Cloning: Difference between revisions
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→The quantum circuit
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* 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> | * 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\Bigg(\sqrt{\frac{1+tan^4\eta}{2}}\Bigg)</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>) | ||
* Reverse Controlled $U_2$ gate: A controlled unitary gates with the <math>x</math> (original) qubit as the control qubit and the <math>y</math> qubit as the operational qubit. The unitary gate <math>U_2</math> acts only if the control qubit is <math>|0\rangle</math>. The unitary <math>U_2</math> is:</br> | * Reverse Controlled $U_2$ gate: A controlled unitary gates with the <math>x</math> (original) qubit as the control qubit and the <math>y</math> qubit as the operational qubit. The unitary gate <math>U_2</math> acts only if the control qubit is <math>|0\rangle</math>. The unitary <math>U_2</math> is:</br> | ||