1211.2549 (A. R. Kuzmak et al.)

Quantum brachistochrone problem for two spins-1/2 with anisotropic
Heisenberg interaction    [PDF]

A. R. Kuzmak, V. M. Tkachuk

We study the quantum brachistochrone evolution for a system of two spins-1/2 describing by an anisotropic Heisenberg Hamiltonian without $zx$, $zy$ interecting couplings in magnetic field directed along z-axis. This Hamiltonian realizes quantum evolution in two subspaces spanned by $|\uparrow\uparrow>$, $|\downarrow\downarrow>$ and $|\uparrow\downarrow>$, $|\downarrow\uparrow>$ separately and allows to consider brachistochrone problem on each subspace separately. Using operator of evolution for this Hamiltonian we generate quantum gates, namely an entanler gate, $SWAP$ gate, $iSWAP$ gate. We also show that the time required for the generation of an entangler gate and $iSWAP$ gate is minimal from all possible.

View original: http://arxiv.org/abs/1211.2549