Spatial Search on Sierpinski Carpet Using Quantum Walk
Shu Tamegai, Shohei Watabe, and Tetsuro Nikuni

TL;DR
This paper explores quantum spatial search on the Sierpinski carpet fractal lattice, supporting the spectral dimension conjecture and proposing a scaling hypothesis for quantum amplitude amplification.
Contribution
It extends the study of quantum search dynamics to the Sierpinski carpet and introduces a new scaling hypothesis for oracle calls.
Findings
Simulation supports the spectral dimension conjecture for the Sierpinski carpet.
Proposes a scaling hypothesis for quantum amplitude amplification.
Provides insights into quantum search on fractal lattices.
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.
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