2008/10/17 by Peter Leifer, Leifer, Peter
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #General Physics (physics.gen-ph) #Noncommutative and Quantum Gravity Theories #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.0810.3188
9 pages, 2 figures, LaTeX
arxiv created 2008/10/17 · openalex publication_date 2008/10/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Cartan control problem of the quantum circuits discussed from the differential geometry point of view. Abstract unitary transformations of SU(2n) are realized physically in the projective Hilbert state space CP(2n-1) of the n-qubit system. Therefore the Cartan decomposition of the algebra AlgSU(2n-1) into orthogonal subspaces h and b such that [h,h] ⊆ h, [b,b] ⊆ h, [b,h] ⊆ b is state-dependent and thus requires the representation in the local coordinates.