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→Quantum SWAP test
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[[File:SWAP_test_figure.png |center|thumb|500px|Figure 9: Gate Teleporation for Multiple Single Qubit Gates]]</div> | [[File:SWAP_test_figure.png |center|thumb|500px|Figure 9: Gate Teleporation for Multiple Single Qubit Gates]]</div> | ||
Quantum SWAP test 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>. | [Quantum SWAP test | https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.87.167902] 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\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. | ||
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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> | 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. | 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. | ||
===Quantum Capable Homomorphic Encryption=== | ===Quantum Capable Homomorphic Encryption=== | ||
*'''Homomorphic Encryption'''<br/>A homomorphic encryption scheme HE is a scheme to carry out classical computation from the Server while hiding the inputs, outputs and computation. It can be divided into following four stages. | *'''Homomorphic Encryption'''<br/>A homomorphic encryption scheme HE is a scheme to carry out classical computation from the Server while hiding the inputs, outputs and computation. It can be divided into following four stages. | ||