Efficiently Generation of Cluster States via Time-Delayed Feedback in Matrix Representation

TL;DR

This paper introduces a matrix-based protocol leveraging time-delayed feedback to efficiently generate arbitrary cluster states in quantum computing, reducing resource usage and addressing practical loss mechanisms.

Contribution

It develops a novel matrix representation for TDF-based cluster state generation and demonstrates a minimal TDF protocol for tree-cluster states.

Findings

Efficient protocol reduces TDF usage for cluster state generation.

Demonstrates a single TDF process for tree-cluster states.

Analyzes loss mechanisms and fidelity in practical implementations.

Abstract

Cluster states, as highly entangled multi-qubit states, are widely used as essential resources for quantum communication and quantum computing. However, due to the diverse requirements of applications for cluster states with specific entanglement structures, a universal generation protocol is still lacking. Here we develop a matrix representation according to the characteristics of time-delayed feedback (TDF) and propose a protocol for generating arbitrary cluster states with multiple TDFs. The matrix representation also allows us to optimize the generation process to reduce TDF usage, thus improving efficiency. In particular, we demonstrate a tree-cluster-state generation process that requires only one TDF. Moreover, accounting for the critical loss mechanisms and imperfections in our protocol, we discuss the additional losses caused by multiple TDFs and evaluate the fidelity of the resulting cluster states.