Quantum Computing with an 'Always On' Heisenberg Interaction

Many promising ideas for quantum computing demand the experimental ability to directly switch 'on' and 'off' a physical coupling between the component qubits. This is typically the key difficulty in implementation, and precludes quantum computation in generic solid state systems, where interactions between the constituents are 'always on'. Here we show that quantum computation is possible in strongly coupled (Heisenberg) systems even when the interaction cannot be controlled. The modest ability of 'tuning' the transition energies of individual qubits proves to be sufficient, with a suitable encoding of the logical qubits, to generate universal quantum gates. Furthermore, by tuning the qubits collectively we provide a scheme with exceptional experimental simplicity: computations are controlled via a single 'switch' of only six settings. Our schemes are applicable to a wide range of physical implementations, from excitons and spins in quantum dots through to bulk magnets.