Quantum random walks on congested lattices and the effect of dephasing

Area of Science:

• Quantum physics
• Condensed matter physics
• Statistical mechanics

Background:

• Classical random walks are fundamental in modeling diffusion and transport.
• Quantum random walks offer potential advantages in speed and exploration.
• Congested lattices with defects present challenges for walker dynamics.

Purpose of the Study:

• To investigate quantum random walks on congested lattices.
• To compare quantum and classical random walk behavior under congestion.
• To analyze the impact of dephasing on quantum walk dynamics.

Main Methods:

• Modeling congested lattices with static defects that reverse walker direction.
• Implementing a dephasing process to interpolate between quantum and classical walks.
• Analyzing walker escape times from finite boundaries.

Main Results:

• Quantum walkers exhibit significantly faster escape times from finite boundaries compared to classical walkers.
• The quantum advantage in escape speed is maintained even in heavily congested lattices.
• Dephasing influences the quantum walk, allowing a smooth transition towards classical behavior.

Conclusions:

• Quantum random walks demonstrate a robust advantage in escaping congested environments.
• The presence of defects and dephasing do not negate the inherent speedup of quantum walkers.
• This study highlights the potential of quantum walks for efficient transport in complex systems.