Entangled dual-rail photonic qubit states are important resource states for measurement-based and fusion-based quantum computing. However, their generation is highly challenging due to the probabilistic nature of entangling operations. Here, the authors introduce a formalism using ZX diagrams to design linear optical systems that can generate entangled multiqubit states of dual-rail photonic qubits. This formalism makes it easier to compare methods for creating a desired photonic state and to find the most optimal one.
Fusion measurements are a key primitive for linear-optical quantum computing and quantum networks. Type-I and type-II fusion gates are widely used to combine small entangled resource states into larger photonic states, but without ancillary resources their success probability is limited to
1/2. Existing
3/4-efficient type-I schemes rely on entangled Bell-pair ancillary states, whose preparation is itself probabilistic and resource-intensive. Here we propose a boosted type-I fusion gate using only four ancillary single photons and standard linear-optical primitives. For multiqubit GHZ and graph states, the gate succeeds directly with probability
5/8, while a distillation protocol converts partially entangled outcomes into additional successful events, raising the total success probability to
11/16 after one stage and asymptotically to
3/4. We quantify the practical advantage of this scheme by estimating the photonic resources required for generating representative large entangled photonic states and show that the proposed gate significantly reduces the required overhead compared with existing schemes. These results expand the set of resource-efficient linear-optical primitives and enable a substantial reduction in the resource requirements for scalable photonic quantum computing and quantum communication.