Generation of topologically useful entangled states

TL;DR

This paper introduces an abstract scheme for efficiently generating 2D and 3D topologically useful entangled states, crucial for measurement-based quantum computation, with scalable grid sizes and applicability to various quantum architectures.

Contribution

The paper proposes a universal, scalable scheme for creating complex entangled states, including 2D, 3D, and topological error correction structures, enhancing quantum resource generation methods.

Findings

Linear scaling of grid size with cluster depth

Capability to generate 3D and topological structures

Relevance to cavity QED architectures

Abstract

Measurement based quantum computation requires the generation of a cluster state (quantum resource) prior to starting a computation. Generation of this entangled state can be difficult with many schemes already proposed. We present an abstract scheme which can create 2D cluster states as a universal resource for quantum computing. We find a linear scaling of grid size with cluster depth. The scheme is also capable of creating more exotic topologies including 3D structures and the unit cell for topological error correction. We note its relevance to the cavity QED scheme in [30] although it could be applied to various architectures.