Adiabatic Quantum Search in Open Systems

TL;DR

This paper investigates the robustness of adiabatic quantum search algorithms in open systems, finding they remain scalable at zero temperature with fast-decaying environmental noise but fail at finite temperature due to scattering effects.

Contribution

It provides a detailed analysis of how environmental coupling affects adiabatic quantum algorithms, highlighting conditions for scalability and limitations at finite temperatures.

Findings

Scalability is maintained at zero temperature with fast low-frequency noise decay.

Finite temperature introduces scattering that hampers quantum speedup.

Results are broadly applicable to various adiabatic quantum algorithms.

Abstract

Adiabatic quantum algorithms represent a promising approach to universal quantum computation. Whilst in a closed system these algorithms are limited by avoided level crossings, where the gap becomes exponentially small in the system size, their robustness in open systems remains unresolved. We study the dynamics in the proximity of such an avoided level crossing associated with the adiabatic quantum search algorithm in a quantum system that is coupled to a generic environment. At zero temperature, we find that the algorithm remains scalable provided the noise spectral density of the environment decays sufficiently fast at low frequencies. At finite temperature, however, scattering processes render the algorithm inefficient and no quantum speedup can be achieved. Owing to the generic nature of our model, we expect our results to be widely applicable to other adiabatic quantum algorithms.