Weighing matrices and optical quantum computing

TL;DR

This paper explores the connection between weighing matrices and the construction of continuous-variable cluster states in optical quantum computing, providing new insights into their structure and related graphs.

Contribution

It establishes a theoretical link between weighing matrices and resource state preparation in optical quantum computing, including new structural results.

Findings

Proved structural properties of weighing matrices

Linked weighing matrices to graph structures in quantum states

Enhanced understanding of resource state construction

Abstract

Quantum computation in the one-way model requires the preparation of certain resource states known as cluster states. We describe how the construction of continuous-variable cluster states for optical quantum computing relate to the existence of certain families of matrices. The relevant matrices are known as weighing matrices, with a few additional constraints. We prove some results regarding the structure of these matrices, and their associated graphs.