Controlled-Z gates with giant atoms in structured waveguides

Giant atoms are quantum emitters coupled to waveguides at multiple, spatially separated points, enabling interference effects that fundamentally change their light-matter interactions. A notable consequence of the interference is the emergence of decoherence-free interaction (DFI), which allows coherent excitation exchange between giant atoms via the waveguide without radiative loss. Leveraging DFI offers a promising route to implementing two-qubit quantum gates without the need for additional resources, positioning giant atoms as a versatile platform for scalable universal quantum simulators. However, existing work has focused primarily on continuous, Markovian waveguides; in structured waveguides, where non-Markovian effects become significant, only iSWAP gates have been explored. To address this gap, we introduce and analyze a protocol for implementing controlled-Z (CZ) gates with giant atoms in structured waveguides. We first show that while a minimal two-point coupling scheme supports DFI, it also exhibits strong non-Markovian effects that substantially degrade gate fidelity. To overcome this limitation, we propose an extended design featuring a third coupling point. This configuration suppresses non-Markovian effects and enables CZ gates with fidelities up to $97.7\%$ (assuming typical values for experimental imperfections). Our results broaden the accessible gate set for giant atoms in structured waveguides to include both iSWAP and CZ gates, advancing these systems as a pathway toward universal quantum simulators operating in non-Markovian environments.