Optimal generation of single-qubit operation from an always-on interaction by algebraic decoupling

We present a direct algebraic decoupling approach to generate arbitrary single-qubit operations in the presence of a constant interaction by application of local control signals. To overcome the difficulty of undesirable entanglement generated by the untunable interaction, we use an algebraic approach to decouple the two-qubit Hamiltonian into two single-qubit Hamiltonians and the desired single-qubit operations are then generated by steering on the single-qubit operation spaces. Specifically, we derive local control fields that are designed to drive the qubit systems back to unentangled states at the end of the time interval over which the desired single-qubit operation is completed. As a result of the decoupling, optimal control strategies may be carried out on single qubit subspaces rather than on the full coupled qubit Hilbert space. This approach is seen to be particularly relevant for the physical implementation of solid-state quantum computation.