Flexible entangled state generation in linear optics

Fault-tolerant quantum computation can be achieved by creating constant-sized, entangled resource states and performing entangling measurements on subsets of their qubits. Linear optical quantum computers can be designed based on this approach, even though entangling operations at the qubit level are non-deterministic in this platform. Probabilistic generation and measurement of entangled states must be pushed beyond the required threshold by some combination of scheme optimisation, introduction of redundancy and auxiliary state assistance. We report progress in each of these areas. We explore multi-qubit fusion measurements on dual-rail photonic qubits and their role in measurement-based resource state generation, showing that it is possible to boost the success probability of photonic GHZ state analysers with single photon auxiliary states. By incorporating generators of basic entangled "seed" states, we provide a method that simplifies the process of designing and optimising generators of complex, encoded resource states by establishing links to ZX diagrams.