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Any single-qubit unitary operation or quantum gate can be considered arotation. Typical experimental implementations of single-qubit gates involvetwo or three fixed rotation axes, and up to three rotation steps. Here we showthat, if the rotation axes can be tuned arbitrarily in a fixed plane, then tworotation steps are sufficient for implementing a single-qubit gate, and onerotation step is sufficient for implementing a state transformation. Theresults are relevant for "exchange-only" logical qubits encoded in three-spinblocks, which are important for universal quantum computation in decoherencefree subsystems and subspaces.

Single-qubit gates in two steps with rotation axes in a single plane