A note on adiabatic theorem for Markov chains and adiabatic quantum computation

TL;DR

This paper derives an adiabatic theorem for Markov chains based on mixing times and discusses its implications for adiabatic quantum computation, connecting classical stochastic processes with quantum algorithms.

Contribution

It introduces a new adiabatic theorem for Markov chains and explores its relevance to recent advances in adiabatic quantum computing.

Findings

Established a link between mixing times and adiabatic evolution.

Provided insights into the application of classical Markov chain theory to quantum computation.

Highlighted potential for improved quantum algorithms using classical stochastic analysis.

Abstract

We derive an adiabatic theorem for Markov chains using well known facts about mixing and relaxation times. We discuss the results in the context of the recent developments in adiabatic quantum computation.