A continuous-time quantum walker on finite Sierpiński carpet lattices is increasingly trapped near its initial corner as fractal order grows, unlike ballistic crossing on a uniform lattice.
Quantum Walks on Sierpinski Gaskets
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abstract
We analyze discrete-time quantum walks on Sierpinski gaskets using a flip-flop shift operator with the Grover coin. We obtain the scaling of two important physical quantities: the mean-square displacement and the mixing time as function of the number of points. The Sierpinski gasket is a fractal that lacks translational invariance and the results differ from those described in the literature for ordinary lattices. We find that the displacement varies with the initial location. Averaged over all initial locations, our simulation obtain an exponent very similar to classical diffusion.
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Quantum walker trapped by self-similarity of the Sierpi\'nski carpet
A continuous-time quantum walker on finite Sierpiński carpet lattices is increasingly trapped near its initial corner as fractal order grows, unlike ballistic crossing on a uniform lattice.