Scaling hypothesis of a spatial search on fractal lattices using a quantum walk

Rei Sato, Tetsuro Nikuni, Shohei Watabe

研究成果: Article査読

3 被引用数 (Scopus)

抄録

We investigate a quantum spatial search problem on fractal lattices, such as Sierpinski carpets and Menger sponges. In earlier numerical studies of the Sierpinski gasket, the Sierpinski tetrahedron, and the Sierpinski carpet, conjectures have been proposed for the scaling of a quantum spatial search problem finding a specific target, which is given in terms of the characteristic quantities of a fractal geometry. We find that our simulation results for extended Sierpinski carpets and Menger sponges support the conjecture for the optimal number of oracle calls, where the exponent is given by 1/2 for ds>2 and the inverse of the spectral dimension ds for ds<2. We also propose a scaling hypothesis for the effective number of oracle calls defined by the ratio of the optimal number of oracle calls to a square root of the maximum finding probability. The form of the scaling hypothesis for extended Sierpinski carpets is very similar but slightly different from the earlier conjecture for the Sierpinski gasket, the Sierpinski tetrahedron, and the conventional Sierpinski carpet.

本文言語English
論文番号022312
ジャーナルPhysical Review A
101
2
DOI
出版ステータスPublished - 2020 2月
外部発表はい

ASJC Scopus subject areas

  • 原子分子物理学および光学

フィンガープリント

「Scaling hypothesis of a spatial search on fractal lattices using a quantum walk」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル