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.