  The design of time-independent local Hamiltonians that realise quantum
algorithms is derived from the study of perfect state transfer. The novel
features of this evolution are the perfect realisation of the computation, and
the ability to implement operations in parallel rather than sequentially. This
is applied to a quantum circuit for concatenated error correcting codes, and
the properties of the eigenstates are compared to those of topological
memories. An erroneous implementation of the algorithm (one where a single
error could lead to a fault in the output) is found not to be topological,
whereas a true fault-tolerant algorithm possesses self-correcting properties,
suggesting the existence of a unifying structure for fault-tolerant memories.
