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