Quantum Phase Estimation and the Aharonov-Bohm effect

TL;DR

This paper links the Aharonov-Bohm effect to quantum phase estimation, showing how physical systems like particles on a ring can implement the algorithm and providing insights into its classical limit.

Contribution

It demonstrates that the Aharonov-Bohm effect can physically realize quantum phase estimation for both abelian and non-abelian cases, offering a more intuitive understanding.

Findings

Implementation of quantum phase estimation via the Aharonov-Bohm effect

Extension to non-abelian Aharonov-Bohm effect for $U(N)$

Analysis of the classical limit using path integrals

Abstract

We consider the time evolution of a particle on a ring with a long solenoid through and show that due to the Aharonov-Bohm effect this system naturally makes up a physical implementation of the quantum phase estimation algorithm for a $U(1)$ unitary operator. The implementation of the full quantum phase estimation algorithm with a $U(N)$ unitary operator is realised through the non-abelian Aharonov-Bohm effect. The implementation allows for a more physically intuitive understanding of the algorithm. As an example we use the path integral formulation of the implemented quantum phase estimation algorithm to analyse the classical limit $\hbar\to0$.