Estimation ยท Algorithms
SWAP test
Theorem statement
For any $n$-qubit states $\ket{\psi}$ and $\ket{\phi}$, the state $\ket{\psi'} = \mathtt{H}_1 \mathtt{CSWAP}\mathtt{H}_1\ket{0,\psi,\phi}$ satisfies
$$
\bra{\psi'}(\ket{1}\!\bra{1}\otimes I^{\otimes 2n})\ket{\psi'}
=
(1-|\langle\psi|\phi\rangle|^2) / 2.
$$
- $\mathtt{H}_1$
- Hadamard gate acting on the control qubit.
- $\mathtt{CSWAP}$
- Controlled-SWAP gate exchanging the two target registers when the control qubit is one.
Sources
- Quantum fingerprinting
Harry Buhrman, Richard Cleve, John Watrous, Ronald de Wolf, 2001
- Stabilization of Quantum Computations by Symmetrization
Adriano Barenco, Andre Berthiaume, David Deutsch, Artur Ekert, Richard Jozsa, Chiara Macchiavello, 1997
Lean context
- Lean declaration
QuantumAlg.SwapTest.main
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