Critically damped quantum search

TL;DR

This paper introduces a damped quantum search algorithm that transitions between quantum and classical search regimes, achieving a fixed-point search with minimal additional queries despite uncertainty about target count.

Contribution

It proposes a novel damping-based modification of Grover's algorithm, identifying a critical damping point and enabling a fixed-point search with improved robustness.

Findings

Identifies a critical damping value separating quantum and classical search regimes.

Develops a fixed-point quantum search algorithm tolerant to unknown number of targets.

Achieves only a 1.5-fold increase in oracle queries under uncertainty.

Abstract

Although measurement and unitary processes can accomplish any quantum evolution in principle, thinking in terms of dissipation and damping can be powerful. We propose a modification of Grover's algorithm in which the idea of damping plays a natural role. Remarkably, we have found that there is a critical damping value that divides between the quantum $O(\sqrt{N})$ and classical O(N) search regimes. In addition, by allowing the damping to vary in a fashion we describe, one obtains a fixed-point quantum search algorithm in which ignorance of the number of targets increases the number of oracle queries only by a factor of 1.5.