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Quantum geometry of the Cartan control problem by Leifer, Peter is a scholarly article available to read on EtoBox.

What is Quantum geometry of the Cartan control problem about?

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.

Author

Leifer, Peter

Published

2008

Language

EN