Fig. 3: Circuit decomposition of the double-excitation gate.
From: Improved strategies for fermionic quantum simulation with global interactions
Circuit decomposition of the double-excitation gate \({U}_{pq}^{rs}(\theta )=\exp (-i\theta {G}_{pq}^{rs})\) using the XX and YY gates. The rotation angle in the circuits is defined as \(\widetilde{\theta }={(-1)}^{m}\theta /4\), where m follows the same distinction between even qubit numbers n = 2m and odd numbers n = 2m + 1 as before. Gates with dashed lines are only required if n is odd. The dots ⋯ labeling the quantum wire bundle represent all qubits affected by the parity string \({{\mathcal{Z}}}_{pq}^{rs}\).
