Definitions for swap test
swap test

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1. Swap test

   The Swap test is a procedure in quantum computation that is used to check how much two quantum states differ.Consider two states: | ϕ ⟩ {\displaystyle |\phi \rangle } and | ψ ⟩ {\displaystyle |\psi \rangle } . The state of the system at the beginning of the protocol is | 0 , ϕ , ψ ⟩ {\displaystyle |0,\phi ,\psi \rangle } . After the Hadamard gate, the state of the system is 1 2 ( | 0 , ϕ , ψ ⟩ + | 1 , ϕ , ψ ⟩ ) {\displaystyle {\frac {1}{\sqrt {2}}}(|0,\phi ,\psi \rangle +|1,\phi ,\psi \rangle )} . The controlled SWAP gate transforms the state into 1 2 ( | 0 , ϕ , ψ ⟩ + | 1 , ψ , ϕ ⟩ ) {\displaystyle {\frac {1}{\sqrt {2}}}(|0,\phi ,\psi \rangle +|1,\psi ,\phi \rangle )} . The second Hadamard gate results in 1 2 ( | 0 , ϕ , ψ ⟩ + | 1 , ϕ , ψ ⟩ + | 0 , ψ , ϕ ⟩ − | 1 , ψ , ϕ ⟩ ) = 1 2 | 0 ⟩ ( | ϕ , ψ ⟩ + | ψ , ϕ ⟩ ) + 1 2 | 1 ⟩ ( | ϕ , ψ ⟩ − | ψ , ϕ ⟩ ) {\displaystyle {\frac {1}{2}}(|0,\phi ,\psi \rangle +|1,\phi ,\psi \rangle +|0,\psi ,\phi \rangle -|1,\psi ,\phi \rangle )={\frac {1}{2}}|0\rangle (|\phi ,\psi \rangle +|\psi ,\phi \rangle )+{\frac {1}{2}}|1\rangle (|\phi ,\psi \rangle -|\psi ,\phi \rangle )} The Measurement gate on the first qubit ensures that it's 0 with a probability of P ( First qubit = 0 ) = 1 2 ( ⟨ ϕ | ⟨ ψ | + ⟨ ψ | ⟨ ϕ | ) 1 2 ( | ϕ ⟩ | ψ ⟩ + | ψ ⟩ | ϕ ⟩ ) = 1 2 + 1 2 | ⟨ ψ | ϕ ⟩ | 2 {\displaystyle P({\text{First qubit}}=0)={\frac {1}{2}}{\Big (}\langle \phi |\langle \psi |+\langle \psi |\langle \phi |{\Big )}{\frac {1}{2}}{\Big (}|\phi \rangle |\psi \rangle +|\psi \rangle |\phi \rangle {\Big )}={\frac {1}{2}}+{\frac {1}{2}}{|\langle \psi |\phi \rangle |}^{2}} when measured. If ψ {\displaystyle \psi } and ϕ {\displaystyle \phi } are orthogonal ( | ⟨ ψ | ϕ ⟩ | 2 = 0 ) {\displaystyle ({|\langle \psi |\phi \rangle |}^{2}=0)} , then the probability that 0 is measured is 1 2 {\displaystyle {\frac {1}{2}}} . If the states are equal ( | ⟨ ψ | ϕ ⟩ | 2 = 1 ) {\displaystyle ({|\langle \psi |\phi \rangle |}^{2}=1)} , then the probability that 0 is measured is 1.

How to pronounce swap test?

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Numerology

1. Chaldean Numerology

   The numerical value of swap test in Chaldean Numerology is: 7

2. Pythagorean Numerology

   The numerical value of swap test in Pythagorean Numerology is: 6

References

1. ^ Wikipedia
   https://en.wikipedia.org/wiki/Swap_Test