Qubit rotation in QHE

TL;DR

This paper explores the Quantum Hall effect's ground state wave function, focusing on topological quantum computation and the role of non-abelian Berry phases in quantum charge pumping.

Contribution

It introduces a topological quantum computation perspective on Quantum Hall states, emphasizing the role of entangled spinors and non-abelian Berry phases.

Findings

Ground state wave function at ν=1 is fundamental for other states.

Non-abelian Berry phase causes quantum pumped charge flow.

Topological aspects are key to understanding Quantum Hall physics.

Abstract

In Quantum Hall effect the ground state wave function at $\nu=1$ is the building block of all other states at different filling factors. It is developed by the entanglement of two spinors forming a singlet state. The inherent frustration visualized by the non-abelian matrix Berry phase is responsible for the quantum pumped charge to flow in the Hall surface. The Physics behind the Quantum Hall states is studied here from the view point of topological quantum computation.