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Supplementary Information: Difference between revisions
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→Gate Teleportation
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<math>|0\rangle _1\otimes H|\psi\rangle _2+|1\rangle _1\otimes X|\psi\rangle _2</math> | <math>|0\rangle _1\otimes H|\psi\rangle _2+|1\rangle _1\otimes X|\psi\rangle _2</math> | ||
<math>|m\rangle \otimes X^mH|\psi\rangle</math></br></br> | <math>|m\rangle \otimes X^mH|\psi\rangle</math></br></br> | ||
Similarly if we have the input state rotated by a <math>\mathrm | Similarly if we have the input state rotated by a <math>\mathrm{Z}(\theta)</math> gate the circuit would look like [[Supplementary Information#2a|Figure 2a]]. As the rotation gate <math>\mathrm{Z}(\theta)</math> commutes with Controlled-Phase gate. Hence, [[Supplementary Information#2b|Figure 2b]] is justified.<br/> | ||
<div id="2"><div id="2a"><div id="2b"><ul> | <div id="2"><div id="2a"><div id="2b"><ul> | ||
<li style="display: inline-block;"> [[File:Modified Input.jpg|frame|500px|2(a)Modified Input]]</li> | <li style="display: inline-block;"> [[File:Modified Input.jpg|frame|500px|2(a)Modified Input]]</li> | ||
<li style="display: inline-block;"> [[File:Gate Teleportation.jpg|frame|500px|2(b)Gate Teleportation]] </li> | <li style="display: inline-block;"> [[File:Gate Teleportation.jpg|frame|500px|2(b)Gate Teleportation]] </li> | ||
</ul></div></div></div><br/> | </ul></div></div></div><br/> | ||
This shows that for a pair of | This shows that for a pair of <math>\mathrm{CZ}</math> entangled qubits, if the second qubit is in <math>|+\rangle</math> state (not an eigen value of <math>\mathrm{Z}</math>) then one can teleport (transfer) the first qubit state operated by any unitary gate <math>\mathrm{U}</math> to the second qubit by performing operations only on the first qubit and measuring it. Next, we would need to make certain Pauli corrections (in this case <math>{\mathrm{X}}^{\mathrm{m}}</math>) to obtain <math>\mathrm{U}|\psi\rangle</math>. In other words, we can say the operated state is teleported to the second qubit by a rotated basis measurement of the first qubit with additional Pauli corrections. | ||
===Graph states=== | ===Graph states=== | ||