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We show that efficient quantum computation is possible using a disorderedHeisenberg spin-chain with `always-on' couplings. Such disorder occursnaturally in nanofabricated systems. Considering a simple chain setup, we showthat an arbitrary two-qubit gate can be implemented using just threerelaxations of a controlled qubit, which amounts to switching the on-siteenergy terms at most twenty-one times.Comment: To appear in Phys. Rev.

Efficient quantum computation within a disordered Heisenberg spin chain