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

Rei Sato, Tetsuro Nikuni, Shohei Watabe

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number022312
JournalPhysical Review A
Volume101
Issue number2
DOIs
Publication statusPublished - 2020 Feb
Externally publishedYes

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Fingerprint

Dive into the research topics of 'Scaling hypothesis of a spatial search on fractal lattices using a quantum walk'. Together they form a unique fingerprint.

Cite this