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Quantum Review Letters

Engineering topological quantum state transfer via quantum metric

Ming-Zhu Xiao, Hai-Tao Ding, Dan-Wei Zhang

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Topological pumping has attracted great attention in topological physics and is highly valuable in the realization of robust quantum state transfer (QST). However, speeding up the topological QST under the requirement of adiabatic evolutions remains challenging. In this work, we propose a geometric adiabatic criterion with an effective quantum metric that characterizes non-adiabatic transitions during evolutions via the quantum metric, minimal energy gap and cycle time. Using two generalized Su–Schrieffer–Heeger models, we systematically validate our adiabatic criterion in optimizing topological pumping paths for transferring single-site states and two-site entangled states, respectively. With numerical simulations, we show that by designing pumping paths for minimizing the effective quantum metric, the fidelity and speed of the QST can be significantly improved. Our works provides a general framework for high-fidelity topological QST via quantum metric optimization.

DOI
10.1016/j.qrl.2026.07.001

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Topological pumping has attracted great attention in topological physics and is highly valuable in the realization of robust quantum state transfer (QST). However, speeding up the topological QST under the requirement of adiabatic evolutions remains challenging. In this work, we propose a geometric adiabatic criterion with an effective quantum metric that characterizes non-adiabatic transitions during evolutions via the quantum metric, minimal energy gap and cycle time. Using two generalized Su–Schrieffer–Heeger models, we systematically validate our adiabatic criterion in optimizing topological pumping paths for transferring single-site states and two-site entangled states, respectively. With numerical simulations, we show that by designing pumping paths for minimizing the effective quantum metric, the fidelity and speed of the QST can be significantly improved. Our works provides a general framework for high-fidelity topological QST via quantum metric optimization.
Efficient adiabatic control schemes, where one steers a quantum system along an adiabatic path ensuring minimal excitations while achieving a desired final state, that enable fast, high-fidelity operations are essential for any practical quantum computation. However, current optimization protocols are not universally tractable due to stringent requirements imposed by the microscopic systems encoding the qubit, including complex energy level structures and unwanted transitions, and generally require a trade-off between speed and fidelity of the operation. Here, we address these challenges by developing a general framework for optimal control based on the quantum metric tensor. This framework allows for fast and high-fidelity adiabatic pulses, even for a dense energy spectrum, based solely on the Hamiltonian of the system instead of the time evolution propagator and independent of the size of the underlying Hilbert space. Furthermore, our framework suppresses diabatic transitions and state-dependent crosstalk effects without the need for additional control fields. As an example, we study the adiabatic charge transfer in a double quantum dot to find optimal control pulses with improved performance. We show that for the geometric protocol, the transfer fidelities are lower bounded F>99%\mathcal{F}>99\%F>99% for ultrafast $20~\mbox{ns}$ pulses, regardless of the size of the anti-crossing, while being robust against miscalibration errors and quasistatic noise.
Robust quantum state transfer (QST) is an indispensable ingredient in scalable quantum information processing. Here we present an experimentally feasible scheme for robust QST via topologically protected edge states in superconducting circuits. Using superconducting X-mon qubits with tunable couplings, the generalized Su-Schrieffer-Heeger models with topological magnon bands can be constructed. A novel entanglement-dependent topological Thouless pumping can be directly observed in this system. More importantly, we show that single-qubit states and entanglement can be robustly transferred with high fidelity in the presence of qubit-coupling imperfection, which is a hallmark of topological protection. This approach is experimentally applicable to a variety of quantum systems.
We propose a fast and robust quantum state transfer protocol employing a Su-Schrieffer-Heeger chain, where the interchain couplings vary in time. Based on simple considerations around the terms involved in the definition of the adiabatic invariant, we construct an exponential time-driving function that successfully takes advantage of resonant effects to speed up the transfer process. Using optimal control theory, we confirm that the proposed time-driving function is close to optimal. To unravel the crucial aspects of our construction, we proceed to a comparison with two other approaches: one where the underlying Su-Schrieffer-Heeger chain is adiabatically time-driven and another where the underlying chain is topologically trivial and resonant effects are at work. By numerically investigating the resilience of each protocol to static noise, we highlight the robustness of the exponential driving.
We present a fast and robust protocol for realizing topological quantum state transfer in a dimeric Su-Schrieffer-Heeger spin chain. By giving a more general condition sufficient for the resonant adiabatic evolution, we develop a method of constructing time-driving functions for topological quantum state transfer, which makes it possible to shorten the needed operation time via resonant adiabatic passage between topologically protected edge states. Compared with previous protocols, our protocol can shorten the operation time appreciably while maintaining robustness against disorder in the spin chain, thereby avoiding decoherence resulting from long-running evolution and increasing transmission efficiency. Numerical simulations demonstrate that our protocol possesses excellent robustness and scalability. Our results provide a promising route for the realization of fast and robust quantum state transfer in spin chain systems.
Gap-protected topological channels are a promising way to realize robust and high-fidelity state transfer in quantum networks. Although various topological transfer protocols based on the Su-Schrieffer-Heeger (SSH) model or its variants have been proposed, the phase accumulation during the evolution, as an essential aspect, is underestimated. Here, by numerically studying the phase information of quantum state transfer (QST) in one-dimensional (1D) topological spin chains, we uncover a universal phase correction ϕ0=(N−1)π/2 for both adiabatic and diabatic topological schemes. Interestingly, the site-number-dependent phase correction satisfies Z4 symmetry and is equally effective for perfect mirror transmission in spin chains. Our work reveals a universal phase correction in 1D topologically protected QST, which will prompt a reevaluation of the topological protection mechanism in quantum systems.
The need for fast and robust quantum state transfer is an essential element in scalable quantum information processing, leading to widespread interest in shortcuts to adiabaticity for speeding up adiabatic quantum protocols. However, shortcuts to adiabaticity for systems with more than a few levels is occasionally challenging to compute in theory and frequently difficult to implement in experiments. In this paper, we develop a protocol for constructing shortcuts to adiabaticity through the multistate Landau-Zener approach and a stricter adiabatic condition. Importantly, our protocol only requires a few pieces of information about the energy spectrum and just adjusts the evolutionary rate of the system. It means that our protocol has broad applicability to theoretical models and does not require increasing the difficulty of the experiment. As examples, we apply our protocol to state transfer in the two-level Landau-Zener model, the non-Hermitian Su-Schrieffer-Heeger model, and the topological Thouless pump model and find that it can speed up the manipulation speed while remaining robust to Hamiltonian errors. Furthermore, based on the experimental friendliness of our findings, it can potentially be extended to many-body systems, dissipation cases, or Floquet processes. Overall, the proposed shortcut protocol offers a promising avenue for enhancing the efficiency and reliability of quantum state transfer protocols.