Resource costs for fault-tolerant linear optical quantum computing

Linear optical quantum computing (LOQC) seems attractively simple: information is borne entirely by light and processed by components such as beam splitters, phase shifters and detectors. However this very simplicity leads to limitations, such as the lack of deterministic entangling operations, which are compensated for by using substantial hardware overheads. Here we quantify the resource costs for full scale LOQC by proposing a specific protocol based on the surface code. With the caveat that our protocol can be further optimised, we report that the required number of physical components is at least five orders of magnitude greater than in comparable matter-based systems. Moreover the resource requirements grow higher if the per-component photon loss rate is worse than one in a thousand, or the per-component noise rate is worse than $10^{-5}$. We identify the performance of switches in the network as the single most influential factor influencing resource scaling.