Perfect quantum state transfer on diamond fractal graphs

TL;DR

This paper introduces a new class of fractal-like quantum spin chains on diamond fractal graphs that enable perfect quantum state transfer, expanding possibilities beyond traditional 1D systems.

Contribution

It presents a novel approach using fractal analysis to design quantum spin networks with perfect state transfer capabilities on complex fractal graphs.

Findings

Supports perfect quantum state transfer on fractal graphs

Combines Dyson hierarchical structure with permutation symmetries

Works across various Hausdorff and spectral dimensions

Abstract

In the quest for designing novel protocols for quantum information and quantum computation, an important goal is to achieve perfect quantum state transfer for systems beyond the well-known one dimensional cases, such as 1d spin chains. We use methods from fractal analysis and probability to find a new class of quantum spin chains on fractal-like graphs (known as diamond fractals) which support perfect quantum state transfer, and which have a wide range of different Hausdorff and spectral dimensions. The resulting systems are spin networks combining Dyson hierarchical model structure with transverse permutation symmetries of varying order.