⚛️ quantum physics

Robust topological quantum state transfer with long-range interactions in Rydberg arrays

This paper proposes a theoretical framework for robust, high-fidelity topological quantum state transfer in one-dimensional Rydberg atom arrays, demonstrating that long-range dipole-dipole interactions enhance energy gaps and improve transfer efficiency against disorder compared to nearest-neighbor models.

Original authors: Siri Raupach, Beatriz Olmos, Mathias B. M. Svendsen

Published 2026-01-28

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Siri Raupach, Beatriz Olmos, Mathias B. M. Svendsen

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you have a long line of people standing in a row, holding hands. Your goal is to pass a secret message (a quantum state) from the person at the very left end to the person at the very right end. In a normal line, if you just whisper the message down the line, it might get lost, distorted, or interrupted by someone bumping into a neighbor.

This paper proposes a smarter, more robust way to do this using a special kind of "magic rope" made of Rydberg atoms (super-excited atoms that act like giant magnets). Here is how the researchers explain their solution using simple concepts:

1. The Problem: The "Crowded Room" vs. The "Special Hallway"

Usually, to move a message across a quantum system, you have to rely on neighbors passing it along one by one. This is slow and fragile; if one person in the middle is slightly out of place (disorder), the message gets stuck or scrambled.

The researchers looked at a special type of "hallway" called a topological system. Think of this like a magical train track that only exists at the very edges of a city. If you put your message on the edge, it is protected by the rules of the city (symmetry). It can't easily fall off the track or get confused by obstacles in the middle of the city. This is called an edge state.

2. The Innovation: The "Long-Range" Superpower

Most previous ideas for these magical tracks only let people talk to the person immediately next to them (nearest-neighbor interactions).

This paper introduces Rydberg atoms, which are special because they can "see" and talk to people far down the line, not just their immediate neighbor. Imagine if everyone in the line could shout to anyone else, but the volume of their shout depended on how far away they were.

The researchers found that these long-range shouts actually make the magic track stronger.

The Analogy: Imagine trying to walk across a bridge. If the bridge is only supported by pillars right next to each other, it might wobble. But if you add long, strong cables connecting the pillars to the far ends of the bridge (long-range interactions), the bridge becomes much stiffer and more stable.
The Result: These long-range connections create a bigger "energy gap" (a wider, safer gap between the safe track and the dangerous middle). This allows the message to travel faster and with higher accuracy than if they only talked to their immediate neighbors.

3. Two Ways to Send the Message

The paper describes two methods to get the message from left to right:

Method A: The "Oscillating Swing" (Time-Independent)
Imagine a swing set. If you push the swing at just the right rhythm, it goes back and forth perfectly between two points. In this method, the message naturally swings back and forth between the left and right edges.
- The Catch: It keeps swinging forever. To stop it exactly at the right person, you have to hit a "pause button" (a sudden change in the system's settings) at the exact moment it reaches the other side. While accurate, this is slow because the swing moves slowly when it's very stable.
Method B: The "Guided Walk" (Time-Dependent/Adiabatic)
Imagine a hiker walking from one side of a valley to the other. Instead of jumping, they slowly change the shape of the valley so the path naturally guides them from the left edge to the right edge.
- The Trick: The researchers found a specific path to walk that avoids the "cliffs" (where the path gets dangerous). Because of the long-range connections (the "cables" mentioned earlier), the valley is wider and safer. This allows the hiker to walk faster without falling off, reaching the other side in record time (microseconds) with near-perfect accuracy (over 99.9%).

4. Why It's Tough to Break (Robustness)

In the real world, things aren't perfect. The atoms might not be placed in exactly the right spots (positional disorder). It's like if the people in the line were standing slightly crooked.

The Finding: Because the message is traveling on a "topological" track (the edge), it doesn't care much if the people in the middle are slightly out of place.
The Surprise: Even though the long-range connections mean that more people are affected by a crooked neighbor, the system actually becomes more robust. The extra stability provided by the long-range "cables" outweighs the confusion caused by the crooked positions.

Summary

The paper claims that by using Rydberg atoms, which can interact over long distances, we can build a quantum "highway" that is:

Faster: The message travels quicker than in standard systems.
More Accurate: It arrives with very little error (high fidelity).
Tougher: It survives better if the atoms are slightly out of place.

They tested this with simulations of chains of atoms (some with an odd number, some with an even number) and found that the long-range interactions are a key ingredient for making quantum state transfer reliable and efficient.

Technical Summary: Robust Topological Quantum State Transfer with Long-Range Interactions in Rydberg Arrays

Problem Statement
Reliable quantum state transfer (QST) between distant nodes is a fundamental requirement for quantum information processing. While numerous protocols exist for platforms like spin chains and superconducting qubits, they often face limitations: time-dependent adiabatic protocols are susceptible to decoherence due to long timescales, while time-independent schemes based on nearest-neighbour models suffer from a trade-off between transfer speed and localization fidelity. Furthermore, the impact of long-range interactions on topological QST remains an open question; while such interactions can destabilize topological phases, they may also offer mechanisms to enhance performance. The authors investigate whether the inherent long-range dipole-dipole interactions in Rydberg atom arrays can be harnessed to improve the speed, efficiency, and robustness of topological QST in one-dimensional systems.

Methodology
The authors develop a theoretical framework modeling chains of Rydberg atoms trapped in optical tweezers. The system operates in the single-excitation regime, mapping the dipole-dipole interactions onto extended Su–Schrieffer–Heeger (eSSH) and extended Rice–Mele (eRM) models.

Hamiltonian Construction: The system is described by a Hamiltonian incorporating all-to-all long-range couplings ( $J_{2m}, J'_{2m-1}$ ) derived from the dipole-dipole interaction formula, dependent on interatomic distances and the alignment angle of transition dipole moments. By tuning the geometric offset of the bipartite lattice (sublattices A and B) and applying a staggered detuning ( $\hbar\Delta$ ), the authors control the effective hopping parameters and symmetry properties.
Symmetry Engineering: The authors analyze conditions for generating single-sided edge states. For even-length chains, they utilize the Rice–Mele model with a sublattice energy offset to break chiral symmetry and lift degeneracy, creating localized edge states. For odd-length chains, chiral symmetry enforces a zero-energy edge state localized at a single boundary.
Protocols: Two transfer strategies are evaluated:
1. Time-Independent: Coherent Rabi oscillations between edge states in even-length eSSH chains, stabilized by a sudden quench of the sublattice energy offset.
2. Time-Dependent: Adiabatic evolution of Hamiltonian parameters (geometric offsets $b, h$ and detuning $\Delta$ ) to transport an excitation from one edge to the other in both odd-length eSSH and even-length eRM chains.
Simulation: Numerical simulations are performed for specific experimental parameters (87Rb atoms, $N=9$ to $N=20$ , lattice spacing $a=12\mu m$ ). Performance is quantified by transfer fidelity ( $F > 99.9\%$ ) and transfer time/velocity. Robustness is tested against positional disorder modeled as Gaussian random displacements.

Key Contributions

Theoretical Framework for Long-Range Topological QST: The paper establishes that long-range dipole-dipole interactions in Rydberg arrays naturally realize extended SSH and Rice–Mele models. It demonstrates that these interactions do not merely degrade topological properties but can be systematically exploited to enhance QST.
Mechanism for Enhanced Efficiency: The authors show that long-range couplings significantly broaden the minimum energy gap between the mid-gap edge state and the bulk spectrum. This gap enhancement allows for faster adiabatic parameter variations while maintaining adiabaticity, directly translating to higher transfer velocities.
Optimized Transfer Protocols: The study identifies specific geometric configurations and optimized parameter paths (non-linear variations of lattice offsets) that maximize transfer fidelity and speed. It contrasts these with linear paths and nearest-neighbour-only models.
Robustness Analysis: The work quantifies the resilience of these protocols against positional disorder, a critical experimental imperfection in Rydberg arrays.

Results

Performance Enhancement: In the odd-length eSSH model, the inclusion of full long-range interactions increases the transfer velocity by approximately 22% compared to nearest-neighbour models for a chain of $N=19$ atoms. Similarly, the extended Rice–Mele model shows up to a 13% velocity enhancement for $N=20$ .
High Fidelity: Optimized adiabatic protocols achieve transfer fidelities exceeding 99.9% with transfer times (e.g., ~19.5 $\mu$ s for $N=9$ ) well within the coherence times of Rydberg states (typically 100 $\mu$ s to 1 ms).
Disorder Resilience: The protocols exhibit strong robustness against positional disorder. For the odd-length SSH chain, fidelities remain above 93% even for disorder strengths up to $\sigma_R = 0.15a$ . Surprisingly, the inclusion of long-range couplings further enhances this robustness, suggesting the gap enhancement outweighs the increased sensitivity to positional fluctuations in coupling terms.
Limitations: The time-independent protocol for even-length chains is limited by long oscillation periods required for high localization, making it less practical than adiabatic methods given finite Rydberg lifetimes. The Rice–Mele protocol shows slightly higher sensitivity to strong disorder ( $\sigma_R > 0.1a$ ) due to the necessity of traversing a topologically trivial regime where protection is temporarily absent.

Significance and Claims
The paper claims that long-range interactions, naturally present in Rydberg atom systems, serve as a valuable resource for topologically assisted quantum state transfer. Contrary to the intuition that long-range couplings might destabilize topological phases, the authors demonstrate that they can be tuned to substantially improve transfer efficiency and robustness. The results highlight the potential of Rydberg arrays as a reliable platform for high-fidelity QST, offering a systematic route to overcome the speed-robustness trade-offs inherent in nearest-neighbour models. The work suggests that the geometric control available in optical tweezer arrays allows for the systematic exploitation of these long-range effects to achieve fast, high-fidelity, and disorder-resilient quantum state transfer.