Continuous-Time Quantum Walk in Glued Trees: Localized State-Mediated Almost Perfect Quantum-State Transfer

Area of Science:

• Quantum physics
• Graph theory
• Information science

Background:

• Quantum walkers are essential for quantum computation and information transfer.
• Graph architecture significantly impacts quantum system dynamics and efficiency.
• Previous studies often focused on regular tree structures, limiting insights into complex architectures.

Purpose of the Study:

• To investigate how the architecture of glued trees influences quantum walker dynamics.
• To understand the efficiency of quantum state transfer between roots in leafier tree structures.
• To explore the relationship between branching rate (M) and root degree (N) on transfer efficiency.

Main Methods:

• Numerical simulations of quantum walker dynamics on glued trees.
• Analysis of the walker's behavior as an isomorphic particle on a finite-size chain with defects.
• Analytical development to study the energy spectrum and localized states.

Main Results:

• Quantum state transfer efficiency is highly dependent on the branching rate (M) relative to the root degree (N).
• The walker's behavior mimics a particle on a defective finite chain, with roots and leaves acting as defects.
• Disparities between M and N lead to quasi-degenerate localized states, enhancing quantum beats and transfer efficiency.

Conclusions:

• The architecture of glued trees, specifically the M/N ratio, critically governs quantum state transfer.
• Localized states formed due to architectural imbalances are key to efficient quantum-state transfer.
• Findings provide insights into quantum information transfer mechanisms on complex graph structures.