Generating redundantly encoded resource states for photonic quantum computing

Measurement-based quantum computing relies on the generation of large entangled cluster states that act as a universal resource on which logical circuits can be imprinted and executed through local measurements. A number of strategies for constructing sufficiently large photonic cluster states propose fusing many smaller resource states generated by a series of quantum emitters. However, the fusion process is inherently probabilistic with a 50% success probability in standard guise. A recent proposal has shown that, in the limit of low loss, the probability of achieving successful fusion may be boosted to near unity by redundantly encoding the vertices of linear graph states using Greenberger-Horne-Zeilinger states [Quantum 7, 992 (2023)]. Here we present a protocol for deterministically generating redundantly encoded photonic resource states using single quantum emitters, and study the impact of protocol errors and photonic losses on the generated resource states and type-II photonic fusion. Our work provides a route for efficiently constructing complex entangled photonic qubit states for photonic quantum computing and quantum repeaters.