Two-walker discrete-time quantum walks on the line with percolation

Area of Science:

• Quantum physics
• Quantum information science
• Condensed matter physics

Background:

• Quantum walks are a key model for quantum computation.
• Exploiting multi-particle quantum phenomena is crucial for quantum computing.
• Lattice imperfections can affect quantum system performance.

Purpose of the Study:

• To investigate the behavior of two non-interacting quantum walkers on a line with lattice imperfections.
• To analyze the impact of static and dynamic percolation on quantum walks.
• To determine how particle symmetry and imperfections influence quantum walk outcomes.

Main Methods:

• Simulating two-particle quantum walks on a one-dimensional lattice.
• Introducing lattice imperfections through missing links (bonds).
• Analyzing statistical and dynamical percolation regimes.
• Examining two-particle quantities and output distributions for varying missing bond probabilities.

Main Results:

• The symmetry of the input state under particle exchange strongly influences the quantum walk's output, even with imperfections.
• Bunching phenomena in output distributions do not reliably reveal walker indistinguishability when averaged.
• The spread of the quantum walk is not significantly altered by adding a second particle.

Conclusions:

• Particle symmetry is a critical factor in multi-particle quantum walks, especially in imperfect systems.
• Averaging quantum walk outputs obscures information about particle indistinguishability.
• Multiple walkers can enhance methods for estimating lattice imperfection probabilities.