Formation of Multipartite Entanglement Using Random Quantum Gates

TL;DR

This paper investigates how multipartite entanglement forms in quantum systems using random gates, comparing local and non-local qubit arrangements, and finds non-local setups generate entanglement more rapidly.

Contribution

It introduces a comparative analysis of entanglement formation in local versus non-local quantum register geometries using random gates.

Findings

Non-local geometry produces faster entanglement growth.

Groverian measure converges more slowly than bipartite entanglement.

Results inform design of future quantum computer architectures.

Abstract

The formation of multipartite quantum entanglement by repeated operation of one and two qubit gates is examined. The resulting entanglement is evaluated using two measures: the average bipartite entanglement and the Groverian measure. A comparison is made between two geometries of the quantum register: a one dimensional chain in which two-qubit gates apply only locally between nearest neighbors and a non-local geometry in which such gates may apply between any pair of qubits. More specifically, we use a combination of random single qubit rotations and a fixed two-qubit gate such as the controlled-phase gate. It is found that in the non-local geometry the entanglement is generated at a higher rate. In both geometries, the Groverian measure converges to its asymptotic value more slowly than the average bipartite entanglement. These results are expected to have implications on different proposed geometries of future quantum computers with local and non-local interactions between the qubits.