  The work presented here extends upon the best known universal quantum
circuit, the Quantum Shannon Decomposition proposed in [Vivek V. Shende,
Stephen S. Bullock and Igor Markov, Synthesis of Quantum Logic Circuits, IEEE
Trans. Comput.-Aided Des. Integr. Circuits Syst. 25 (6): 1000-1010 (2006)]. We
obtain the basis of the circuit's design in a pair of Cartan decompositions.
This insight gives a simple constructive algorithm for obtaining the Quantum
Shannon Decomposition of a given unitary matrix in terms of the corresponding
Cartan involutions.
