  We show how to implement quantum computation on a system with an intrinsic
Hamiltonian by controlling a limited subset of spins. Our primary result is an
efficient control sequence on a nearest-neighbor XY spin chain through control
of a single site and its interaction with its neighbor. Control of an array of
sites yields sufficient parallelism for the implementation of fault-tolerant
circuits. The framework exposes contradictions between the control theoretic
concept of controllability with the ability of a system to perform quantum
computation.
