Constructive quantum Shannon decomposition from Cartan involutions

2008/06/25 by Byron Drury, Peter J. Love · 1 citation
Chemistry · Computer Science · Mathematics · Physics and Astronomy · #Algebra over a field #Chemistry #Computer science #Constructive #Decomposition #Mathematics #Physics #Programming language #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #quant-ph

paper · pdf · doi:10.1088/1751-8113/41/39/395305

arxiv created 2008/06/25 · openalex publication_date 2008/09/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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.

Citations

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Cited by

• GULPS: Two-Qubit Gate Synthesis via Linear Programming for Heterogeneous Instruction Sets