Non-Abelian geometric phases in a system of coupled quantum bits

TL;DR

This paper extends the concept of Abelian geometric phases to non-Abelian phases in quantum bits, proposing a method to measure these phases in a controllable four-qubit system, advancing quantum information processing techniques.

Contribution

It introduces a generalized approach to measure non-Abelian geometric phases using a cyclic four-qubit chain with controllable interactions.

Findings

Method for measuring non-Abelian geometric phases in four-qubit systems

Generalization of the 'orange slice' path to non-Abelian phases

Feasible implementation in controllable quantum systems

Abstract

A common strategy to measure the Abelian geometric phase for a qubit is to let it evolve along an 'orange slice' shaped path connecting two antipodal points on the Bloch sphere by two different semi- great circles. Since the dynamical phases vanish for such paths, this allows for direct measurement of the geometric phase. Here, we generalize the orange slice setting to the non-Abelian case. The proposed method to measure the non-Abelian geometric phase can be implemented in a cyclic chain of four qubits with controllable interactions.