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Advanced Quantum Technologies

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

Jin‐Xuan Han, Jin‐Lei Wu, Yan Wang, Yan Xia, Yongyuan Jiang, Jie Song

Published Aug 20, 2025• 2 citations
Publisher

Abstract

Abstract 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.

DOI
10.1002/qute.202500362

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Abstract 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.
Topological pumping of edge states in the finite lattice with nontrivial topological phases provides a powerful means for robust excitation transfer, requiring extremely slow evolution to follow an adiabatic transfer. Here, we propose fast topological pumping via edge channels to generate large-scale Greenberger-Horne-Zeilinger (GHZ) states in a topological superconducting circuit with a sped-up evolution process. The scheme indicates a conceptual way of designing fast topological pumping related to the instantaneous energy spectrum characteristics rather than relying on the shortcuts to adiabaticity. Based on fast topological pumping, large-scale GHZ states show greater robustness against on-site potential defects, the fluctuation of couplings and losses of the system in comparison with the conventional adiabatic topological pumping. With experimentally feasible qutrit-resonator coupling strengths and moderate decay rates of qutrits and resonators, fast topological pumping drastically improves the scalability of GHZ states with a high fidelity. Our work opens up prospects for the realization of large-scale GHZ states based on fast topological pumping in the superconducting quantum circuit system, which provides potential applications of topological matters in quantum information processing.
We propose a superconducting qutrit-resonator chain model, and analytically work out forms of its topological edge states. The existence of the zero-energy mode enables one to generate a state transfer between two ends of the chain, accompanied with state flips of all intermediate qutrits, based on which NNN-body Greenberger-Horne-Zeilinger (GHZ) states can be generated with great robustness against disorders of coupling strengths. Three schemes of generating large-scale GHZ states are designed, each of which possesses the robustness against loss of qutrits or of resonators, meeting a certain performance requirement of different experimental devices. With experimentally feasible qutrit-resonator coupling strengths and available coherence times of qutrits and resonators, it has a potential to generate large-scale GHZ states among dozens of qutrits with a high fidelity. Further, we show the experimental consideration of generating GHZ states based on the circuit QED system, and discuss the prospect of realizing fast GHZ states.
The Su–Schrieffer–Heeger (SSH) model, commonly used for robust state transfers through topologically protected edge pumping, has been generalized and exploited to engineer diverse functional quantum devices. Here, we propose to realize a fast topological beam splitter based on a generalized SSH model by accelerating the quantum state transfer (QST) process essentially limited by adiabatic requirements. The scheme involves delicate orchestration of the instantaneous energy spectrum through exponential modulation of nearest neighbor coupling strengths and onsite energies, yielding a significantly accelerated beam splitting process. Due to properties of topological pumping and accelerated QST, the beam splitter exhibits strong robustness against parameter disorders and losses of system. In addition, the model demonstrates good scalability and can be extended to two-dimensional crossed-chain structures to realize a topological router with variable numbers of output ports. Our work provides practical prospects for fast and robust topological QST in feasible quantum devices in large-scale quantum information processing.
Engineering synthetic dimensions, where the physics of additional spatial dimensions is simulated within the internal states of a quantum system, allows the realisation of phenomena not otherwise accessible in experiments. Ultracold ground-state polar molecules are an ideal platform to encode synthetic dimensions, offering access to large Hilbert spaces of long-lived internal states associated with the rotational and hyperfine degrees of freedom, that can be coupled together with microwave fields to simulate tunnelling. Here, to benchmark the advantages of ultracold molecules, we encode a 1D synthetic lattice in the rotational states of ultracold RbCs molecules and use it to investigate the well-known Su-Schrieffer-Heeger (SSH) model, a minimal model displaying topological properties. To probe the system, we perform spectroscopy using an auxiliary rotational state and study the time dynamics after deterministic state preparation. We demonstrate long coherence times, typically ~500 times the lattice tunnelling period, even for a synthetic lattice using 8 rotational states. Observations of dynamics at long times with full site-resolved readout of the synthetic dimension allow us to test the effects of chiral and non-chiral perturbations on the topologically protected edge states. Our work lays the foundation for further quantum simulations using the rich internal structure of molecules, including dipolar string phases in interacting samples of molecules, and adiabatic state preparation of many-body Hamiltonians.
Rydberg-atom synthetic dimensions in the form of a lattice of n3S1^3S_13S1​ levels, 58≤n≤6358\leq n \leq 6358≤n≤63, coupled through two-photon microwave excitation are used to examine dynamics within the single-particle Su-Schrieffer-Heeger (SSH) Hamiltonian. This paradigmatic model of topological matter describes a particle hopping on a one-dimensional lattice with staggered hopping rates. Tunneling rates between lattice sites and on-site potentials are set by the microwave amplitudes and detuning, respectively. An atom is first excited to a Rydberg state that lies within the lattice and then subject to the microwave dressing fields. After some time, the dressing fields are turned off and the evolution of the population distribution in the different final lattice sites monitored using field ionization. The measurements show the existence of long-lived symmetry-protected edge states and reveal the existence of direct long-distance tunneling between the edge states. The results are in good agreement with model calculations and further demonstrate the potential of Rydberg-atom synthetic dimensions to simulate and faithfully reproduce complex Hamiltonians.
Abstract A discrete degree of freedom can be engineered to match the Hamiltonian of particles moving in a real-space lattice potential. Such synthetic dimensions are powerful tools for quantum simulation because of the control they offer and the ability to create configurations difficult to access in real space. Here, in an ultracold 84 Sr atom, we demonstrate a synthetic-dimension based on Rydberg levels coupled with millimeter waves. Tunneling amplitudes between synthetic lattice sites and on-site potentials are set by the millimeter-wave amplitudes and detunings respectively. Alternating weak and strong tunneling in a one-dimensional configuration realizes the single-particle Su-Schrieffer-Heeger (SSH) Hamiltonian, a paradigmatic model of topological matter. Band structure is probed through optical excitation from the ground state to Rydberg levels, revealing symmetry-protected topological edge states at zero energy. Edge-state energies are robust to perturbations of tunneling-rates that preserve chiral symmetry, but can be shifted by the introduction of on-site potentials.