One-dimensional quantum walks with a position-dependent coin

Rashid Ahmad,Uzma Sajjad,Muhammad Sajid

Figure 3. Standard deviation (σ) versus the number of steps of the walk for T = 30. (a) The dashed red line shows the standard deviation of a simple classical random walk ($\sigma =\sqrt{T}$). The dotted blue line represents a bounded classical-like walk, the solid blue line represents a normal classical-like walk, and the dashed blue line represents a fast classical-like walk. (b) The dotted red line shows the standard deviation of a simple Hadamard walk with position-independent coin ($\sigma \approx T$). The dotted blue line represents a bounded semi-classical-like walk, the solid blue line represents a normal semi-classical-like walk, and the dashed blue line represents a fast semi-classical-like walk. (c) The dotted red line shows the standard deviation of a simple Hadamard walk with a position-independent coin ($\sigma \approx T$). The dotted blue line represents a bounded quantum-like walk.