Editing Glossary (section)

===Gate Teleportation=== 
The idea comes from one-qubit teleporation. This means that one can transfer an unknown qubit |ψi without actually sending it via a quantum channel. The underlying equations explain the notion. See [[Supplementary Information#1|Figure 1]] for circuit.<br/>
<div id="1">
 [[File:One Bit Teleportation.jpg|right|thumb|1000px|Figure 1: One Bit Teleportation]]
</div><math>(H\otimes I)(CZ_{12})|\psi\rangle_1|+\rangle_2</math>
<math>(H\otimes I)(CZ_{12})(a|0\rangle_1+b|1\rangle_1)|+\rangle_2</math>
<math> (H\otimes I)(a|0\rangle_1|+\rangle_2+b|1\rangle_1|-\rangle_2)</math>
<math>a|+\rangle_1|+\rangle_2+b|-\rangle_1|-\rangle_2</math>
<math>|0\rangle_1\otimes(a|+\rangle_2+b|-\rangle_2)+|1\rangle_1\otimes(a|+\rangle_2-b|-\rangle_2)</math>
<math>|0\rangle_1\otimes(a|+\rangle_2+b|-\rangle_2)+|1\rangle_1\otimes X(a|+\rangle_2+b|-\rangle_2)</math>
<math>|0\rangle_1\otimes H(a\rangle 0\rangle _2+b\rangle 1\rangle _2)+|1\rangle _1\otimes XH(a|0\rangle _2+b|1\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>
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>
<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>
</ul></div></div></div><br/>
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.