  Single photons, manipulated using integrated linear optics, constitute a
promising platform for universal quantum computation. A series of increasingly
efficient proposals have shown linear-optical quantum computing to be formally
scalable. However, existing schemes typically require extensive adaptive
switching, which is experimentally challenging and noisy, thousands of photon
sources per renormalized qubit, and/or large quantum memories for
repeat-until-success strategies. Our work overcomes all these problems. We
present a scheme to construct a cluster state universal for quantum
computation, which uses no adaptive switching, no large memories, and which is
at least an order of magnitude more resource-efficient than previous passive
schemes. Unlike previous proposals, it is constructed entirely from
loss-detecting gates and offers a robustness to photon loss. Even without the
use of an active loss-tolerant encoding, our scheme naturally tolerates a total
loss rate of $\sim 1.6\%$ in the photons detected in the gates. This scheme
uses only 3-GHZ states as a resource, together with a passive linear-optical
network. We fully describe and model the iterative process of cluster
generation, including photon loss and gate failure. This demonstrates that
building a linear optical quantum computer need be less challenging than
previously thought.
