Effects of dissipation in an adiabatic quantum search algorithm

TL;DR

This paper investigates how different environmental interactions, including thermal and structured environments, affect the performance of an adiabatic quantum search algorithm, revealing that structured environments can sometimes enhance performance.

Contribution

It demonstrates that structured environments can improve quantum search performance under certain conditions, contrasting with thermal environments that always degrade it.

Findings

Thermal environments worsen algorithm performance across all regimes.

Structured environments can enhance performance when tuned properly.

Complex dissipation rates significantly influence system dynamics.

Abstract

We consider the effect of two different environments on the performance of the quantum adiabatic search algorithm, a thermal bath at finite temperature, and a structured environment similar to the one encountered in systems coupled to the electromagnetic field that exists within a photonic crystal. While for all the parameter regimes explored here, the algorithm performance is worsened by the contact with a thermal environment, the picture appears to be different when considering a structured environment. In this case we show that, by tuning the environment parameters to certain regimes, the algorithm performance can actually be improved with respect to the closed system case. Additionally, the relevance of considering the dissipation rates as complex quantities is discussed in both cases. More particularly, we find that the imaginary part of the rates can not be neglected with the usual argument that it simply amounts to an energy shift, and in fact influences crucially the system dynamics.