Layer by layer generation of cluster states

TL;DR

This paper presents efficient, deterministic methods for generating cluster states on a qubus quantum computer, optimizing the number of operations needed with different strategies for destroying links.

Contribution

It introduces new algorithms for building cluster states with reduced operations, including schemes that allow or prevent link destruction, improving efficiency over naive methods.

Findings

Over 2x reduction in operations compared to naive methods

Schemes with and without link destruction offer different trade-offs

Practical modular generation methods for cluster states

Abstract

Cluster states can be used to perform measurement-based quantum computation. The cluster state is a useful resource, because once it has been generated only local operations and measurements are needed to perform universal quantum computation. In this paper, we explore techniques for quickly and deterministically building a cluster state. In particular we consider generating cluster states on a qubus quantum computer, a computational architecture which uses a continuous variable ancilla to generate interactions between qubits. We explore several techniques for building the cluster, with the number of operations required depending on whether we allow the ability to destroy previously created controlled-phase links between qubits. In the case where we can not destroy these links, we show how to create an n x m cluster using just 3nm -2n -3m/2 + 3 operations. This gives more than a factor of 2 saving over a naive method. Further savings can be obtained if we include the ability to destroy links, in which case we only need (8nm-4n-4m-8)/3 operations. Unfortunately the latter scheme is more complicated so choosing the correct order to interact the qubits is considerably more difficult. A half way scheme, that keeps a modular generation but saves additional operations over never destroying links requires only 3nm-2n-2m+4 operations. The first scheme and the last scheme are the most practical for building a cluster state because they split up the generation into the repetition of simple sections.