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arXiv:2305.14529 · Chinese Physics B

Topological State Transfer through Effective Boundary-Mode Channels

Chong Wang, Gu Xiu, Shu Chen, Yu-xi Liu

Published Oct 30, 2026• 1 citation
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Abstract

Abstract Localized edge modes provide a compact channel for transferring an excitation through an extended lattice, but the relation between the microscopic chain and the few levels that actually govern the transfer is often left implicit. We develop this boundary-subspace description for a superconducting-qubit realization of the Rice–Mele model in the single-excitation sector. For one finite chain, projection onto the two edge modes yields a Landau–Zener Hamiltonian whose detuning and hybridization identify the adiabatic transfer path and the spectral constraint relevant to protocol optimization. We then join two Rice–Mele segments at a single physical boundary qubit. The resulting three localized modes form an effective three-state channel with microscopically determined, independently tunable energies and couplings. This channel supports both a zero-energy dark-state passage and an open Rice–Mele-type passage driven by time-dependent bonds and onsite potentials. Direct simulations of the complete qubit chains reproduce the effective-channel dynamics. Under matched control bounds, dividing the transport distance at a shared boundary also preserves larger finite-size edge-mode couplings and reaches a stable high-fidelity regime faster than transfer through one uninterrupted chain. The boundary-mode projection thus relates the microscopic controls directly to the effective energies, finite-size couplings, and adiabatic gaps that govern the transfer.

DOI
10.1088/1674-1056/aebba8

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Abstract Localized edge modes provide a compact channel for transferring an excitation through an extended lattice, but the relation between the microscopic chain and the few levels that actually govern the transfer is often left implicit. We develop this boundary-subspace description for a superconducting-qubit realization of the Rice–Mele model in the single-excitation sector. For one finite chain, projection onto the two edge modes yields a Landau–Zener Hamiltonian whose detuning and hybridization identify the adiabatic transfer path and the spectral constraint relevant to protocol optimization. We then join two Rice–Mele segments at a single physical boundary qubit. The resulting three localized modes form an effective three-state channel with microscopically determined, independently tunable energies and couplings. This channel supports both a zero-energy dark-state passage and an open Rice–Mele-type passage driven by time-dependent bonds and onsite potentials. Direct simulations of the complete qubit chains reproduce the effective-channel dynamics. Under matched control bounds, dividing the transport distance at a shared boundary also preserves larger finite-size edge-mode couplings and reaches a stable high-fidelity regime faster than transfer through one uninterrupted chain. The boundary-mode projection thus relates the microscopic controls directly to the effective energies, finite-size couplings, and adiabatic gaps that govern the transfer.
We develop a theoretical framework for fast, robust and high-fidelity topological quantum state transfer in one-dimensional systems with long-range couplings, motivated by chains of Rydberg atoms with dipole-dipole interactions. Such long-range interactions naturally give rise to extended Su-Schrieffer-Heeger and Rice-Mele models supporting topologically protected edge states. We show that these edge states enable high-fidelity edge-to-edge excitation transfer using both time-independent protocols, based on coherent edge state dynamics, and time-dependent protocols, based on adiabatic modulation of system parameters. Long-range couplings play a central role by enhancing the relevant energy gaps, leading to a substantial improvement in transfer efficiency compared to nearest neighbour models. The resulting transfer is robust against positional disorder, reflecting its topological origin and highlighting the potential of long-range interacting platforms for reliable quantum state transfer.
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 investigate the interacting, one-dimensional Rice-Mele model, a prototypical fermionic model of topological properties. To set the stage, we first compute the single-particle spectral function, the local density, and the boundary charge in the absence of interactions. We find that the fractional part of the boundary charge is fully determined by bulk properties of the lattice model. In a large parameter regime the boundary charge agrees with the one obtained from an effective low-energy theory (arXiv:2004.00463). Second, we investigate the robustness of our results towards two-particle interactions. To resume the series of leading logarithms for small gaps, which dismantle plain perturbation theory in the interaction, we use an essentially analytical renormalization group approach. It is controlled for small interactions and can directly be applied to the microscopic lattice model. We benchmark the results against numerical density matrix renormalization group data. The main interaction effect in the bulk is a power-law renormalization of the gap with an interaction dependent exponent. The important characteristics of the fractional part of the boundary charge are unaltered and can be understood from the renormalized bulk properties. This requires a consistent treatment not only of the low-energy gap renormalization but also of the high-energy band width one. In contrast to low-energy field theories our renormalization group approach also provides the latter. We show that the interaction spoils the relation between the bulk properties and the number of edge states, consistent with the observation that the Rice-Mele model with finite potential modulation does not reveal any zero-energy edge states.
We propose the generation of entangled qubits by utilizing the properties of edge states appearing at one end of a periodically driven (Floquet) superconducting qubit chain. Such qubits are naturally protected by the system's topology and their manipulation is possible through adiabatic control of the system parameters. By utilizing a Y-junction geometry, we then develop a protocol to perform high-fidelity transfer of entangled qubits from one end to another end of a qubit chain. Our quantum state transfer protocol is found to be robust against disorder and imperfection in the system parameters. More importantly, our proposed protocol also performs remarkably well at larger system sizes due to nonvanishing gaps between the involved edge states and the bulk states, thus allowing us in principle to transfer entangled states over an arbitrarily large distance. This work hence indicates that Floquet topological edge states are not only resourceful for implementing quantum gate operations, but also useful for high-fidelity and long-distance transfer of entangled states along solid-state qubit chains.
We theoretically investigate the interplay of topology and localized non-Hermiticity in a finite Su-Schrieffer-Heeger chain characterized by non-Hermitian potentials at its boundaries. By tuning the boundary gain and loss parameters, we exploit the finite-size hybridization of two mid-gap topological edge states to analytically derive the exact coordinates of boundary-induced exceptional points (EPs), ΓEP=±ivN/wN−1Γ_{\rm EP}=\pm i v^{N}/w^{N-1}ΓEP​=±ivN/wN−1, at which these states undergo coalescence. We demonstrate that dynamically encircling these boundary EPs facilitates a robust, chiral edge state-transfer protocol. Depending on the orientation of the encircling loop, this protocol allows a topological edge state localized at one boundary to be either transferred to the opposite edge with perfect fidelity or returned to its starting position through a double switching process. Importantly, since the non-Hermiticity remains strictly confined to the boundaries, this chiral transport occurs without affecting the energy spectrum of the bulk bands. These results establish a minimal framework for a large-scale topological chiral switch that is experimentally verifiable and capable of being controlled through boundary non-Hermitian driving.
Spin chains have been widely studied as quantum channels for short-distance communication in quantum devices, where many-body dynamics can mediate quantum-state transfer between distant sites. In finite unmodulated chains, however, dispersion and interference effects associated with the static Hamiltonian often limit the achievable transfer fidelity. Here we investigate the transfer of single-qubit and Bell states in finite XXXXXX spin chains under periodic switching between two Hamiltonians with different boundary couplings. Inspired by Parrondo's paradox, we examine whether alternating between two configurations that individually yield suboptimal transfer fidelities can generate enhanced coherent transmission. Using Floquet theory together with numerical simulations in the single-excitation subspace, we show that periodic driving can outperform static configurations and achieve higher transfer fidelities. This enhancement originates from the noncommutativity of the driven Hamiltonians and reflects a purely coherent interference effect. We further analyze the dependence of the protocol on system size and driving parameters and examine its robustness to asymmetric boundary couplings. Our results show that the transfer fidelity remains stable under moderate disorder, indicating that simple time-dependent control of boundary couplings provides an effective strategy to enhance quantum-state transfer in spin-chain communication channels and optimize quantum information processing in engineered many-body systems.