Recent works by Brown et al (2005 J. Phys. A: Math. Gen. 38 1119) and Borras et al (2007 J. Phys. A: Math. Theor. 40 13407) have explored numerical optimization procedures to search for highly entangled multi-qubit states according to some computationally tractable entanglement measure. We present an alternative scheme based upon the idea of searching for states having not only high entanglement but also simple algebraic structure. We report results for 4, 5, 6, 7 and 8 qubits discovered by this approach, showing that many of such states do exist. In particular, we find a maximally entangled 6-qubit state with an algebraic structure simpler than the best results known so far. For the case of 7 qubits, we discover states with high, but not maximum, entanglement and simple structure, as well as other desirable properties. Some preliminary results are shown for the case of 8 qubits.
@article(SS-JPhysA-09, author = "Juan E. Tapiador and J. C. Hernandez-Castro and John A. Clark and Susan Stepney", title = "Highly entangled multi-qubit states with simple algebraic structure", journal = "Journal of Physics A: Mathematical and Theoretical", volume = 42, pages = "415301", year = 2009 )