Topological Walks Exhibit Robust, Size-Dependent Quantum Transport Dynamics.

The behaviour of quantum particles within constrained systems continues to yield nuanced insights into fundamental physics and potential technological applications. Recent research focuses on the interplay between topological properties and finite system size in one-dimensional quantum walks, a mathematical model used to simulate quantum particle movement. These walks, unlike their classical counterparts, exhibit behaviours governed by the principles of quantum mechanics, including superposition and entanglement.

Andrzej Grudka, Marcin Karczewski, Paweł Kurzyński, Tomasz P. Polak, Jan Wójcik, and Antoni Wójcik, all from the Institute of Spintronics and Quantum Information at Adam Mickiewicz University, detail their investigation into these phenomena in the article, “Rabi transport and the other finite-size effects in one-dimensional discrete-time topological quantum walk”. Their work demonstrates how the boundaries of a finite system induce localised quantum states and influence the overall dynamics of the walk, transitioning behaviour from ballistic motion to localised or oscillatory patterns.

Andrzej Grudka, Jakub Świerkowski, and Tomasz Sowiński from Adam Mickiewicz University in Poznań, Poland, investigate the dynamics of quantum particles within specifically designed one-dimensional lattices. Their work centres on discrete-time quantum walks, a quantum analogue of classical random walks, and explores how topological properties influence particle transport and are affected by the finite size of the system. The researchers demonstrate the emergence of topologically distinct regions within the lattice, characterised by states confined to its boundaries, and analyse how these boundaries impact the overall walk dynamics.

The study leverages principles of topology to engineer lattices mimicking topological insulators, materials that conduct electricity along their surfaces but remain insulating internally. These lattices support robust edge states, quantum states localized at the boundaries of the material, which are inherently resistant to imperfections and disorder. The analytical framework employed constructs and solves the tight-binding Hamiltonian, a mathematical model describing the energy levels and interactions of particles within the lattice, enabling prediction of system behaviour and identification of key dynamic parameters.

The researchers demonstrate that Rabi transport arises from the coupling between these edge states located at opposite boundaries of the lattice, effectively establishing a pathway for information transfer. This coupling facilitates a periodic exchange of probability between the edge states, resulting in coherent transport across the lattice. Validation of these analytical predictions is achieved through numerical simulations, employing techniques such as the transfer matrix method and time evolution of wave packets to visualise wave function propagation and quantify the efficiency of Rabi transport.

Notably, the robustness of Rabi transport against disorder is a key finding. The introduction of random variations in lattice parameters demonstrates that transport remains largely unaffected, highlighting the topological protection afforded to the edge states. This resilience is crucial for potential applications in quantum information processing, where maintaining the coherence of quantum states is paramount. The team’s work bridges the gap between theoretical predictions and experimental observations by carefully considering finite-size effects and disorder, ensuring relevance to real-world systems.

The study reveals how localized and bilocalized states emerge in finite lattices due to the interplay between topology and finite size. These states give rise to Rabi-like transport, characterised by the periodic exchange of probability between the edge states. Analytical calculations and numerical simulations confirm that this transport is robust against disorder, even with moderate imperfections in the lattice. The researchers demonstrate that the efficiency of Rabi transport is influenced by lattice parameters, with symmetric lattices and well-separated edge states exhibiting optimal performance.

The findings have important implications for the development of robust quantum devices. Topological protection can shield quantum states from decoherence, a major obstacle to building practical quantum computers, and Rabi-like transport can efficiently transfer information between different parts of a quantum circuit. The team plans to explore the possibility of using topological quantum walks to build more complex quantum circuits and to investigate the effects of different types of disorder on the efficiency of Rabi transport, furthering the potential for practical applications.