Geometrical aspects of quantum walks on random two-dimensional structures

Area of Science:

• Quantum physics
• Condensed matter physics
• Complex systems

Background:

• Continuous-time quantum walks (CTQWs) are a quantum analogue of classical random walks.
• Understanding transport properties in finite disordered systems is crucial for quantum technologies.
• The influence of structural geometry, specifically aspect ratios, on quantum transport is not fully understood.

Purpose of the Study:

• To investigate and compare the transport properties of CTQWs and classical continuous-time random walks (CTRWs) on finite 2D lattices.
• To analyze the impact of varying aspect ratios and the number of random bonds on transport efficiency.
• To elucidate the underlying mechanisms, such as eigenstate localization, governing quantum transport in these structures.

Main Methods:

• Simulating CTQWs and CTRWs on 2D lattices with varying aspect ratios and random bond configurations.
• Analyzing the long-time average of the survival probability to quantify transport efficiency.
• Calculating participation ratios of average eigenstates to identify localized versus delocalized states.

Main Results:

• For small aspect ratios, CTQWs and CTRWs exhibit similar transport properties, requiring a comparable number of bonds.
• As aspect ratios increase, CTQWs necessitate a substantially larger number of bonds for efficient transport compared to CTRWs.
• Eigenstate localization, indicated by participation ratios, increases for CTQWs on high aspect ratio structures, hindering transport.

Conclusions:

• The geometric configuration (aspect ratio) significantly impacts the efficiency of quantum transport.
• CTQWs exhibit distinct transport behaviors from CTRWs, particularly in non-square geometries.
• Eigenstate localization is a key factor limiting quantum transport efficiency in disordered 2D systems with high aspect ratios.