Quantum geometry of the Cartan control problem

Abstract

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… (More)

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