Quantum computing with an always-on Heisenberg interaction

Many promising schemes for quantum computing (QC) involve switching on and off a physical coupling between qubits. This may prove extremely difficult to achieve experimentally. Here we show that systems with a constant Heisenberg coupling can be employed for QC if we actively tune the transition energies of individual qubits. Moreover, we can collectively tune the qubits to obtain an exceptionally simple scheme: 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.