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→Quantum SWAP test
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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 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. SWAP test | 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> | 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> | ||