Is the Measurement Based Quantum Computing Search Algorithm Really Grover's Algorithm?

TL;DR

This paper critically examines whether the measurement-based quantum computing search algorithm is truly Grover's algorithm, highlighting fundamental differences especially in larger search spaces, despite superficial similarities in small cases.

Contribution

The study provides a detailed comparison of measurement-based quantum search and Grover's algorithm, revealing key operational differences beyond trivial cases.

Findings

Significant differences in oracle tag behavior

Distinct entanglement dynamics between the algorithms

Fundamental divergence in larger search spaces

Abstract

We question whether the measurement based quantum computing algorithm is in fact Grover's algorithm or simply a similar oracular search method. The two algorithms share several qualitative features especially in the case of the trivial 4 element search, which is the largest size photonic search algorithm that has been experimentally implemented to date. This has led some to refer to both substantiations as Grover's algorithm. We compare multiple features of the two algorithms including the behavior of the oracle tags and the entanglement dynamics, both qualitatively and quantitatively. We find significant and fundamental differences in the operation of the two algorithms, particularly in cases involving searches on more than four elements.