theory to discuss benefits and drawbacks of different potential architectures for a modular quantum computer. A graph-theoretic approach allows us to flexibly examine a wide range of possible arrangements quantitatively and allows for convenient numerical simulation using existing software packages designed for network analysis [@NetworkX]. We especially wish to focus on families of graphs that can scale with the desired number of qubits. In general, we assume that connectivity, i.e., being able to quickly perform operations between nodes, is desirable in an architecture, but that building additional graph edges is in some way costly or difficult, and so will try to minimize the number of needed edges to achieve a highly communicative graph.

We will examine the performance of graphs in generating large entangled states such as the multi-qubit Greenberger-Horne-Zeilinger (GHZ) state (also known as a cat state). The GHZ state has perfect quantum correlations between different qubits; it thus can be used to perform high-precision metrology [@Bollinger1996; @Eldredge2016]. In addition, the creation of a GHZ state can be used as part of a state-transfer protocol, which may be useful as part of large quantum computations [@Eldredge2017].

An additional property of GHZ state preparation and state transfer which makes them 