Spatial Search on Sierpinski Carpet Using Quantum Walk

Abstract

We investigate a quantum spatial search problem on a fractal lattice. A recent study for the Sierpinski gasket and tetrahedron made a conjecture that the dynamics of the search on a fractal lattice is determined by spectral dimension. We tackle this problem for the Sierpinski carpet, and our simulation result supports the conjecture. We also propose a scaling hypothesis of oracle calls for the quantum amplitude amplification.

6 pages, 5 figures

References in corpus (1)

• Search on a Hypercubic Lattice through a Quantum Random Walk: II. d=2

Cited by in corpus (4)

• Complex Quantum Networks: a Topical Review
• Scaling Hypothesis of Spatial Search on Fractal Lattice Using Quantum Walk
• Quantum walks with spatiotemporal fractal disorder
• Universal scaling hypothesis of quantum spatial search in complex networks