Fig. 4: Two equivalent ways to decompose the arbitrary excitation-preserving two-qubit gate defined in Eq. (1) into single-qubit Z rotations and the fundamental entangler F(θ, ϕ) = e−iθ(X⊗X+Y⊗Y)/2−iϕZ⊗Z/4. | npj Quantum Information

Fig. 4: Two equivalent ways to decompose the arbitrary excitation-preserving two-qubit gate defined in Eq. (1) into single-qubit Z rotations and the fundamental entangler F(θ, ϕ) = e−iθ(X⊗X+Y⊗Y)/2−iϕZ⊗Z/4.

From: Characterizing coherent errors using matrix-element amplification

Fig. 4

While the differential phases ζ± = (ζ ± χ)/2 do not commute with F(θ, ϕ), the symmetric phase \({\gamma }^{{\prime} }=\gamma +\phi /2\) does and can be placed either before or after the entangling operation.

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