Extracting photonic graph states from weighted graphs using single-qubit measurements

Graph states are the backbone of quantum communication and measurement-based quantum computation. However, the creation of graph states is extremely challenging because of the lack of photon-photon interactions. Using emitters to mediate such interactions is a promising approach, but errors in the resulting gates lead to states with less entanglement, such as weighted graph states. We propose a protocol where we extract perfect graph states from weighted graph states by using a few single-qubit measurements via entanglement concentration. These protocols are devised using a combination of numerics and tensor network analysis.