Efficient Large‐Scale Entanglement with Domain‐Divided Topological Synthetic Dimension

The notion of synthetic dimensions in artificial systems has received considerable attention as it provides novel methods for exploring hypothetical topological matter as well as potential device applications. A superconducting qutrit‐resonator chain is mapped into domain‐divided Su‐Schrieffer–Heeger (SSH) models in the synthetic dimension formed by product states of qutrits and Fock states, which renders single‐excitation transfers to mimic particle transports in 1D potential array. Large‐scale Greenberger–Horne–Zeilinger (GHZ) states can be generated in one‐domain SSH model of synthetic dimension via the topological protected edge channel. Uniquely, a two‐domain SSH model is constructed, and the wave function of the three topological protected states is analytically derived. It is shown that the effective coherent‐tunneling adiabatic passage (CTAP) enables fast large‐scale GHZ state can be generated via topological CTAP. Furthermore, four‐ and multi‐domain SSH models are identified to generate large‐scale GHZ states faster in larger sizes. Numerical results show that topologically generated large‐scale GHZ states exhibit excellent robustness against inevitable variation in ideal hopping rates and losses of systems. The work opens up prospects for realizing fast large‐scale GHZ states in multiple SSH models of synthetic dimension and for facilitating further applications of topological matter in quantum information processing.