Hilbert Space Average Method and adiabatic quantum search

TL;DR

This paper explores the Hilbert space Average Method as an alternative way to model open quantum system dynamics, extending it to time-dependent Hamiltonians and analyzing its effectiveness in adiabatic quantum search under environmental influence.

Contribution

The paper derives a new form of the Hilbert space Average Method without relying on operator algebra and applies it to time-dependent Hamiltonians in open quantum systems.

Findings

The method effectively models open quantum system dynamics.

Performance analysis of adiabatic quantum search with environmental effects.

Validation criteria for the method's applicability to different environments.

Abstract

We discuss some aspects related to the so-called Hilbert space Average Method, as an alternative to describe the dynamics of open quantum systems. First we present a derivation of the method which does not make use of the algebra satisfied by the operators involved in the dynamics, and extend the method to systems subject to a Hamiltonian that changes with time. Next we examine the performance of the adiabatic quantum search algorithm with a particular model for the environment. We relate our results to the criteria discussed in the literature for the validity of the above-mentioned method for similar environments.