Spatial Search on Sierpinski Carpet Using Quantum Walk

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.