Constructive Quantum Shannon Decomposition from Cartan Involutions

Details Constructive Quantum Shannon Decomposition from Cartan Involutions Constructive Quantum Shannon Decomposition from Cartan Involutions

2008-06-25

arxiv.org/abs/0806.4015v1

Physics

Quantum Physics

Scientific paper

10.1088/1751-8113/41/39/395305

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.

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