Geometry of the adiabatic theorem

TL;DR

This paper provides a clear, geometrically grounded derivation of the quantum adiabatic theorem specifically for two-level systems, emphasizing minimal geometric structures for educational clarity.

Contribution

It offers a simple, pedagogical derivation of the quantum adiabatic theorem for qubits using minimal geometric structures from quantum mechanics.

Findings

Derivation based on geometrical structures of quantum mechanics

Focus on two-level systems (qubits)

Emphasis on minimal geometric framework

Abstract

We present a simple and pedagogical derivation of the quantum adiabatic theorem for two level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for an understanding of the adiabatic theorem for this case.