Topological insulators have inspired the study with various quantum simulators. Exploiting the tunability of the qubit frequency and qubit-qubit coupling, we show that a superconducting qubit chain can simulate various topological band models. When the system is restricted to the single-spin excitation subspace, the Su-Schrieffer-Heeger (SSH) model can be equivalently simulated by alternating the coupling strength between neighboring qubits. The existence of topological edge states in this qubit chain is demonstrated in the quench dynamics after the first qubit is excited. This excitation propagates along the chain where the qubit-qubit coupling is homogeneous. In contrast, in our qubit chain, the spin-up state localizes at the first qubit and the rest qubits remain in the spin-down state. We further show that the spin-up state can be transported along the chain by modulating the coupling strengths and the qubit frequencies. This demonstrates adiabatic pumping based on the Rice-Mele model. Moreover, we also discuss possible ways to construct other topological models with different topological phenomena within the current technology of superconducting qubits.
Topological insulators have inspired the study with various quantum simulators. Exploiting the tunability of the qubit frequency and qubit-qubit coupling, we show that a superconducting qubit chain can simulate various topological band models. When the system is restricted to the single-spin excitation subspace, the Su-Schrieffer-Heeger (SSH) model can be equivalently simulated by alternating the coupling strength between neighboring qubits. The existence of topological edge states in this qubit chain is demonstrated in the quench dynamics after the first qubit is excited. This excitation propagates along the chain where the qubit-qubit coupling is homogeneous. In contrast, in our qubit chain, the spin-up state localizes at the first qubit and the rest qubits remain in the spin-down state. We further show that the spin-up state can be transported along the chain by modulating the coupling strengths and the qubit frequencies. This demonstrates adiabatic pumping based on the Rice-Mele model. Moreover, we also discuss possible ways to construct other topological models with different topological phenomena within the current technology of superconducting qubits.
We propose a protocol using a tunable Xmon qubit chain to construct generalized Su-Schrieffer-Heeger (SSH) models that support various topological phases. We study the time evolution of a single-excitation quantum state in a SSH-type qubit chain and find that such dynamics is linked to the topological winding number. We also investigate the adiabatic transfer of a single-excitation quantum state in a generalized SSH-type qubit chain and show that this process can be connected with the topological Chern number and be used to generate an entanglement-dependent topological pumping. All results have been demonstrated to be robust against qubit coupling imperfections and can be observed in a short Xmon qubit chain. Our study provides a simple method to directly measure topological invariants rooted in momentum space using quantum dynamics in real space.
Topological insulator lie at the forefront of condensed matter physics. However strong disorder can destroy the topological states and make all states become localized. In this paper, we investigate the competition between topology and localization in the one-dimensional Su-Schrieffer-Heeger (SSH) model with controllable off-diagonal quasi-periodic modulations on superconducting circuits. By utilizing external ac magnetic fluxes, each transmon can be driven and all coupling strengths can be tuned independently. Based on this model we construct phase diagrams that illustrate the extended topologically nontrivial, critical localization, and coexisting topological and critical localization phases. The dynamics of the qubits' excitations are also discussed in this paper, revealing distinct quantum state transfers resulting from the interplay between topology and localization. Furthermore, we propose a method for detecting different quantum phases using current experimental setups.
Topological insulators occupy a prominent position in the realm of condensed matter physics. Nevertheless, the presence of strong disorder has the potential to disrupt the integrity of topological states, leading to the localization of all states. This study delves into the intricate interplay between topology and localization within the one-dimensional Su–Schrieffer–Heeger (SSH) model, which incorporates controllable off-diagonal quasi-periodic modulations on superconducting circuits. Through the application of external alternating current (ac) magnetic fluxes, each transmon undergoes controlled driving, enabling independent tuning of all coupling strengths. Within a framework of this model, we construct comprehensive phase diagrams delineating regions characterized by extended topologically nontrivial states, critical localization, and co-existing topological and critical localization phases. The paper also addresses the dynamics of qubit excitations, elucidating distinct quantum state transfers resulting from the intricate interplay between topology and localization. Additionally, we propose a method for detecting diverse quantum phases utilizing existing experimental setups.
Robust quantum state transfer (QST) is an indispensable ingredient in scalable quantum information processing. Here we present an experimentally feasible mechanism for realizing robust QST via topologically protected edge states in superconducting qubit chains. Using superconducting Xmon qubits with tunable couplings, we construct generalized Su-Schrieffer-Heeger models and analytically derive the wave functions of topological edge states. We find that such edge states can be employed as a quantum channel to realize robust QST between remote qubits. With a numerical simulation, we show that both single-qubit states and two-qubit entangled states can be robustly transferred in the presence of sizable imperfections in the qubit couplings. The transfer fidelity demonstrates a wide plateau at the value of unity in the imperfection magnitude. This approach is general and can be implemented in a variety of quantum computing platforms.
Abstract The Su–Schrieffer–Heeger (SSH) model, which captures the most striking transport properties of the conductive organic polymer trans -polyacetylene, provides perhaps the most basic model system supporting topological excitations. The alternating bond pattern of polyacetylene chains is captured by the bipartite sublattice structure of the SSH model, emblematic of one-dimensional chiral symmetric topological insulators. This structure supports two distinct nontrivial topological phases, which, when interfaced with one another or with a topologically trivial phase, give rise to topologically protected, dispersionless boundary states. Here, using 87 Rb atoms in a momentum-space lattice, we realize fully tunable condensed matter Hamiltonians, allowing us to probe the dynamics and equilibrium properties of the SSH model. We report on the experimental quantum simulation of this model and observation of the localized topological soliton state through quench dynamics, phase-sensitive injection, and adiabatic preparation.
Topological gapless systems, as the connection of the different topological quantum phases, have received much attention. Topological nonmediocre nodes are typically observed in two- or three-dimensional gapless systems. In this paper, we demonstrate that the topological nonmediocre nodes are existent in a model that lies between one dimension and two dimensions. Superconducting circuits, as essential all-solid state quantum devices, have offered a promising platform for studying the macro-controlling quantum effects. Recently, experimental achievements have enabled the realization of tunable coupling strengths between transmon qubits and the implementation of a one-dimensional Su-Schrieffer-Heeger (SSH) model [Li X et al. 2018 Phys. Rev. Appl. 10 054009 ]. According to this work, herein we present a two-leg SSH model implemented in superconducting circuits and demonstrate the existence of topological nonmediocre nodes. Firstly, two-leg superconducting circuit with transmon qubits which are coupled with their nearest-neighbor sites by capacitors is designed. To construct the two-leg SSH model, we introduce two alternating-current magnetic fluxes to drive each transmon qubit. We discover two types of phase boundaries in the SSH model and obtain the corresponding energy spectra and phase diagram. We identify two distinct topological insulating phases characterized by winding number ±1, and the corresponding edge states exhibit distinct characteristics. Moreover, we discuss the topological properties of the two phase boundaries. By representing the Bloch states as a vector field in k space, we demonstrate the existence of two kinks of nonmediocre nodes with first-type phase boundaries. These two nonmediocrenodes possess distinct topological charges of 1 and –1, respectively. On the other hand, the nonmediocre nodes with the second-type phase boundaries are topologically trivial. These results open the way for exploring novel topological states, ladder physical systems, and nodal point topological semimetals.