Scale invariance of entanglement dynamics in Grover's quantum search algorithm

TL;DR

This paper investigates the entanglement dynamics in Grover's quantum search algorithm, revealing scale invariance in multipartite entanglement as the number of qubits grows large, and compares it with fixed-point search.

Contribution

It demonstrates that entanglement dynamics in Grover's algorithm are scale-invariant for large qubit numbers and explores implications for simulatability.

Findings

Genuine multipartite entanglement is always present in Grover's algorithm.

Entanglement dynamics are independent of the number of qubits for large n.

Comparison with fixed-point quantum search shows different entanglement behaviors.

Abstract

We calculate the amount of entanglement of the multiqubit quantum states employed in the Grover algorithm, by following its dynamics at each step of the computation. We show that genuine multipartite entanglement is always present. Remarkably, the dynamics of any type of entanglement as well as of genuine multipartite entanglement is independent of the number n of qubits for large n, thus exhibiting a scale invariance property. We compare this result with the entanglement dynamics induced by a fixed-point quantum search algorithm. We also investigate criteria for efficient simulatability in the context of Grover's algorithm.