Computation on Spin Chains with Limited Access
arXiv:0905.4070 · doi:10.1103/PhysRevA.81.010301
Abstract
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.
4 pages, 1 figure v2: added error analysis and supporting numerics; v3: corrected minor errors
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