  In principle a 1D array of nearest-neighbour linked qubits is compatible with
fault tolerant quantum computing. However such a restricted topology
necessitates a large overhead for shuffling qubits and consequently the fault
tolerance threshold is far lower than in 2D architectures. Here we identify a
middle ground: a 1D segmented chain which is a linear array of segments, each
of which is a well-connected zone with all-to-all connectivity. The
architecture is relevant to both ion trap and solid-state systems. We establish
that fault tolerance can be achieved either by a surface code alone, or via an
additional concatenated four-qubit gauge code. We find that the fault tolerance
threshold is 0.12% for 15-qubit segments, while larger segments are superior.
For 35 or more qubits per segment one can achieve computation on a meaningful
scale with today's state-of-the-art fidelities without the use of the upper
concatenation layer, thus minimising the overall device size.
