Minimizing resource overhead in fusion-based quantum computation using hybrid spin-photon devices

We present three schemes for constructing a (2,2)-Shor-encoded 6-ring photonic resource state for fusion-based quantum computing, each relying on a different type of photon source. We benchmark these architectures by analyzing their ability to achieve the loss tolerance threshold for fusion-based quantum computation using the target resource state. More precisely, we estimate their minimum hardware requirements for fault-tolerant quantum computation in terms of the number of photon sources to achieve on-demand generation of resource states with a desired generation period. Notably, we find that a group of 12 deterministic single-photon sources containing a single matter qubit degree of freedom can produce the target resource state near-deterministically by exploiting entangling gates that are repeated until success. The approach is fully modular, eliminates the need for lossy large-scale multiplexing, and reduces the overhead for resource-state generation by several orders of magnitude compared to architectures using heralded single-photon sources and probabilistic linear-optical entangling gates. Our work shows that the use of deterministic single-photon sources embedding a qubit substantially shortens the path toward fault-tolerant photonic quantum computation.