Fast graph operations in quantum computation

TL;DR

This paper introduces a quantum data structure based on graph states that enables more efficient graph manipulation and comparison than classical methods, with proven performance advantages.

Contribution

It presents novel quantum algorithms for graph operations and demonstrates their superiority over classical data structures in certain tasks.

Findings

Quantum graph data structure outperforms classical in manipulation and comparison

Efficient algorithms for graph transformations using quantum states

Classical structures cannot match quantum performance for all studied operations

Abstract

The connection between certain entangled states and graphs has been heavily studied in the context of measurement-based quantum computation as a tool for understanding entanglement. Here we show that this correspondence can be harnessed in the reverse direction to yield a graph data structure which allows for more efficient manipulation and comparison of graphs than any possible classical structure. We introduce efficient algorithms for many transformation and comparison operations on graphs represented as graph states, and prove that no classical data structure can have similar performance for the full set of operations studied.