Deterministic Entanglement as a Prerequisite for Scalable Quantum Photonic Resource State Generation

As demonstrated experimentally by Prevedel et al., active feed-forward can render one-way quantum computation deterministic. An analogous principle applies to the scalable generation of photonic resource states: because each probabilistic photonic fusion operation branches the construction process, the overall success probability shrinks exponentially unless entanglement is generated deterministically. A simple comparative combinatorial resource estimate illustrates the practical consequences of this principle. State-of-the-art fault-tolerant optical quantum computing architectures incur an unreasonably high single-photon overhead when relying solely on probabilistic fusion. In contrast, deterministic sources of entangled multi-photon states, such as semiconductor quantum dots, can reduce the number of required attempts dramatically. Assuming realistic system efficiencies, on average only 15 attempts are needed to generate a 4-qubit resource state (4-star), and 89 attempts for a 6-qubit state (6-ring), bringing efficient resource state generation in reach with near-term photonic systems.