Quantum geometry of the Cartan control problem

Details Quantum geometry of the Cartan control problem Quantum geometry of the Cartan control problem

2008-10-17

arxiv.org/abs/0810.3188v1

Physics

General Physics

9 pages, 2 figures, LaTeX

Scientific paper

The Cartan control problem of the quantum circuits discussed from the differential geometry point of view. Abstract unitary transformations of $SU(2^n)$ are realized physically in the projective Hilbert state space $CP(2^n-1)$ of the n-qubit system. Therefore the Cartan decomposition of the algebra $AlgSU(2^n-1)$ into orthogonal subspaces $h$ and $b$ such that $[h,h] \subseteq h, [b,b] \subseteq h, [b,h] \subseteq b$ is state-dependent and thus requires the representation in the local coordinates.

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