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 $SU(2^n)$ 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.

9 pages, 2 figures, LaTeX

References in corpus (1)

• A geometric approach to quantum circuit lower bounds