Editing Glossary (section)

===Quantum SWAP test===
 <div id="swap">
[[File:SWAP_test_figure.png |center|thumb|500px|Figure 9: Gate Teleporation for Multiple Single Qubit Gates]]</div>

[https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.87.167902  Quantum SWAP test (1) ] helps to compare two quantum states <math>|\psi\rangle</math> and <math>|\psi'\rangle</math>. An ancilla qubit is prepared here in the state <math>\frac{|0\rangle + |1\rangle}{2}</math> and a controlled swap test is performed on two states <math>|\psi\rangle</math> and <math>|\psi'\rangle</math>.

If <math>|\psi\rangle</math> = <math>|\psi'\rangle</math>, then the ancilla qubit, after performing a Hadamard operation, yields <math>|0\rangle</math> when measurement is applied in computational basis. The SWAP test passes here.

If <math>|\psi\langle|\psi'\rangle \leq \delta</math>, then the ancilla qubit, after performing a Hadamard Gate and upon measurement, passes the test with probability <math>\frac{1+\delta^2}{2}</math>
and fails the test with probability  <math>\frac{1-\delta^2}{2}</math>. Hence, the SWAP test always passes for the same inputs and sometimes fails if they are different. By repeating the SWAP test, its efficiency can be amplified.