Fig. 8: Circuit decomposition of the controlled single-excitation gate.
From: Improved strategies for fermionic quantum simulation with global interactions
Circuit decomposition of the controlled single-excitation gate \({U}_{pj}^{qj}(\theta )=\exp (-i\theta {G}_{pj}^{qj})\) using the XX gate in terms of two MS gates and two CjRz gates. The dots ⋯ labeling the quantum wire bundle represent all qubits affected by the parity string \({{\mathcal{Z}}}_{p}^{q}\), except j if p < j < q. The light-gray dashed gates are used if the number of qubits in the wire bundle is odd. The signs in brackets account for the sign flip for p < j < q.
