Adiabatic Theorem for Discrete Time Evolution

TL;DR

This paper proves an adiabatic theorem applicable to quantum systems evolving in discrete time steps, such as quantum maps and circuits, extending the understanding of adiabatic processes beyond continuous evolution.

Contribution

It provides the first rigorous proof of the adiabatic theorem for discrete-time quantum evolution, filling a gap in quantum theory.

Findings

Validates adiabatic approximation for discrete quantum systems

Extends adiabatic theorem to quantum maps and circuits

Provides mathematical framework for discrete adiabatic processes

Abstract

A proof of the adiabatic theorem for quantum systems whose time evolution proceeds along discrete time, e.g., quantum maps and quantum circuits, is shown.