# Analog Nature of Quantum Adiabatic Unstructured Search

## TL;DR

This paper investigates the robustness of the quantum adiabatic unstructured search algorithm, revealing that its quadratic speedup is generally fragile against various imperfections such as control limitations, Hamiltonian errors, and thermal interactions.

## Contribution

It provides a comprehensive analysis of how different non-idealities affect the performance and speedup of the quantum adiabatic unstructured search algorithm.

## Key findings

- Quadratic speedup is not robust to control imperfections.
- Hamiltonian misspecification undermines the algorithm's advantage.
- Thermal interactions can eliminate the quantum speedup.

## Abstract

The quantum adiabatic unstructured search algorithm is one of only a handful of quantum adiabatic optimization algorithms to exhibit provable speedups over their classical counterparts. With no fault tolerance theorems to guarantee the resilience of such algorithms against errors, understanding the impact of imperfections on their performance is of both scientific and practical significance. We study the robustness of the algorithm against various types of imperfections: limited control over the interpolating schedule, Hamiltonian misspecification, and interactions with a thermal environment. We find that the unstructured search algorithm's quadratic speedup is generally not robust to the presence of any one of the above non-idealities, and in some cases we find that it imposes unrealistic conditions on how the strength of these noise sources must scale to maintain the quadratic speedup.