  With gate error rates in multiple technologies now below the threshold
required for fault-tolerant quantum computation, the major remaining obstacle
to useful quantum computation is scaling, a challenge greatly amplified by the
huge overhead imposed by quantum error correction itself. We propose a
fault-tolerant quantum computing scheme that can nonetheless be assembled from
a small number of experimental components, potentially dramatically reducing
the engineering challenges associated with building a large-scale
fault-tolerant quantum computer. Our scheme has a threshold of 0.39% for
depolarising noise, assuming that memory errors are negligible. In the presence
of memory errors, the logical error rate decays exponentially with
$\sqrt{T/\tau}$, where $T$ is the memory coherence time and $\tau$ is the
timescale for elementary gates. Our approach is based on a novel procedure for
fault-tolerantly preparing three-dimensional cluster states using a single
actively controlled qubit and a pair of delay lines. Although a circuit-level
error may propagate to a high-weight error, the effect of this error on the
prepared state is always equivalent to that of a constant-weight error. We
describe how the requisite gates can be implemented using existing technologies
in quantum photonic and phononic systems. With continued improvements in only a
few components, we expect these systems to be promising candidates for
demonstrating fault-tolerant quantum computation with a comparatively modest
experimental effort.
