Computation on spin chains with limited access
Alastair Kay, Peter J. Pemberton-Ross · Physical Review A · 2010
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 $\mathit{XY}$ 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.