quantum gate directory

SDK Support

SDK	Name
Qiskit	—
PennyLane	—
Cirq	cirq.FSimGate
Q#	—
PyQuil	pyquil.simulation.matrices.FSIM
Braket	—
BQSKit	bqskit.ir.gates.FSIMGate

The fermionic simulator gate is a two-parameter family that unifies the iSWAP and CZ interactions.

$$ \mathrm{FSim}(\theta, \phi) = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & \cos\theta & -i\sin\theta & 0 \\ 0 & -i\sin\theta & \cos\theta & 0 \\ 0 & 0 & 0 & \mathrm{e}^{-i\phi} \end{bmatrix} $$

Special cases

• $\mathrm{FSim}(\pi/2, 0) = i\mathrm{SWAP}$
• $\mathrm{FSim}(\pi/4, 0) = \sqrt{i\mathrm{SWAP}}$
• $\mathrm{FSim}(\pi/2, \pi) = \mathrm{fSWAP}$
• $\mathrm{FSim}(0, \phi) = \mathrm{C}P(\phi)$
• $\mathrm{FSim}(0, \pi) = \mathrm{CZ}$
• $\mathrm{FSim}(\pi/2, \pi/6)$ approximates the Sycamore gate used in Google's quantum supremacy experiment.

Properties

• The $\theta$ parameter controls the swap angle in the ${|01\rangle, |10\rangle}$ subspace.
• The $\phi$ parameter is a controlled phase on $|11\rangle$.
• Reduces to a product of single-qubit gates at $\theta = 0, \phi = 0$.