Universal Superposition of Orthogonal States: Difference between revisions
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*'''Output:''' <math>|\Psi_2\rangle = \alpha|1\rangle X|\psi^\perp\rangle |\psi\rangle + \beta |0\rangle |\psi\rangle |\psi^\perp\rangle</math> | *'''Output:''' <math>|\Psi_2\rangle = \alpha|1\rangle X|\psi^\perp\rangle |\psi\rangle + \beta |0\rangle |\psi\rangle |\psi^\perp\rangle</math> | ||
*At this stage the following gates will be performed respectively: | *At this stage the following gates will be performed respectively: | ||
**'''S gate (Controled Swap):''' Performing this gate will interchange the input qubits. The total states before and after performing this gate are as follows: | |||
<math>|\Psi_0\rangle = \alpha|1\rangle |\psi\rangle |\psi^\perp\rangle + \beta |0\rangle |\psi\rangle |\psi^\perp\rangle</math | #<math>|\Psi_0\rangle = \alpha|1\rangle |\psi\rangle |\psi^\perp\rangle + \beta |0\rangle |\psi\rangle |\psi^\perp\rangle</math> | ||
<math>|\Psi_1\rangle = \alpha|1\rangle |\psi^\perp\rangle |\psi\rangle + \beta |0\rangle |\psi\rangle |\psi^\perp\rangle</math | #<math>|\Psi_1\rangle = \alpha|1\rangle |\psi^\perp\rangle |\psi\rangle + \beta |0\rangle |\psi\rangle |\psi^\perp\rangle</math> | ||
**'''CNOT gate:''' The total state after this step is as follows: | |||
<math>|\Psi_2\rangle = \alpha|1\rangle X|\psi^\perp\rangle |\psi\rangle + \beta |0\rangle |\psi\rangle |\psi^\perp\rangle</math> | #<math>|\Psi_2\rangle = \alpha|1\rangle X|\psi^\perp\rangle |\psi\rangle + \beta |0\rangle |\psi\rangle |\psi^\perp\rangle</math> | ||
'''<u>Stage 2</u>''' Measurements</br></br> | '''<u>Stage 2</u>''' Measurements</br></br> | ||