quantum gate directory
fSWAP
Symbol
$\mathrm{fSWAP}$
Description:
Swaps $|01\rangle$ and $|10\rangle$ while applying a $-1$ phase to $|11\rangle$.
The fermionic SWAP (fSWAP) gate behaves like SWAP on single-excitation states, but adds a phase of $-1$ to the $|11\rangle$ state. The name comes from the fact that exchanging two fermions introduces a $-1$ phase as fermionic wavefunctions are antisymmetric under particle exchange.
$$ \mathrm{fSWAP} = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & -1 \end{bmatrix} $$
Properties
- Self-inverse: $\mathrm{fSWAP}^2 = I$.
- Equals SWAP on the ${|01\rangle, |10\rangle}$ subspace.
Groups
This gate is contained in the following groups:
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