Adaptive strategies for graph state growth in the presence of monitored errors

*Physical Review A* **75**, 042303 (2007)

Graph states, also known as cluster states, are the entanglement resource that enables one-way quantum computing. They can be grown by a series of projective measurements on the component qubits. Such measurements typically carry a significant failure probability. Moreover, even upon success they may generate imperfect entanglement. Here we describe strategies to adapt growth operations in order to cancel incurred errors. Nascent states that initially deviate from the ideal graph states evolve toward the desired high fidelity resource without incurring an impractical overhead. Our analysis extends the diagrammatic language of graph states to include characteristics such as tilted vertices, weighted edges, and partial fusion, which may arise due to experimental imperfections. The strategies we present are relevant to parity projection schemes such as optical `path erasure' with distributed matter qubits.