Quantum Control via Geometry: An explicit example

Details Quantum Control via Geometry: An explicit example Quantum Control via Geometry: An explicit example

2008-08-23

arxiv.org/abs/0808.3212v1

Physics

Quantum Physics

6 pages, 2 figures. accepted into PRA

Scientific paper

10.1103/PhysRevA.78.032327

We explicitly compute the optimal cost for a class of example problems in geometric quantum control. These problems are defined by a Cartan decomposition of $su(2^n)$ into orthogonal subspaces $\mathfrak{l}$ and $\mathfrak{p}$ such that $[\mathfrak{l},\mathfrak{l}] \subseteq \mathfrak{p}, [\mathfrak{p},\mathfrak{l}] = \mathfrak{p}, [\mathfrak{p},\mathfrak{p}] \subseteq \mathfrak{l}$. Motion in the $\mathfrak{l}$ direction are assumed to have negligible cost, where motion in the $\mathfrak{p}$ direction do not. In the special case of two qubits, our results correspond to the minimal interaction cost of a given unitary.

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