Exact gate sequences for universal quantum computation using the XY interaction alone

The gate sequences to implement universal quantum computation were constructed using the anisotropic exchange (XY) interaction alone. It allowed defining the qubits as truncated qutrits and resulted in quantum logic elements containing at most seven XY-exchange operations for encoded single-qubit operations and five XY operations for encoded two-qubit gates. A possible layout for the qubits in a triangular arrangement was also proposed.