Under mild conditions the experimentally accessible Hamiltonians of N coupled, yet discernable, spin-1/2 ensembles are shown to allow for generation of the entire Lie group SU(2N). This is the case e.g. in nuclear magnetic resonance (NMR) spectroscopy. Thus quantum computing gates may conveniently be implemented by unitary propagators, viz the `rf-pulse sequences' in NMR spectroscopy.

The maximum achievable coherence transfer amplitude under reversible Hamiltonian dynamics of spin ensembles translates into a minimum Euclidean distance: the minimal distance between the unitary orbit of some given initial ensemble state represented by a density operator (or its signal-relevant components collected in a matrix A that need no longer be hermitian) and a given final state or observable (or its components C).

Given two arbitrary matrices A,C, the first computer algorithm is presented for a gradient minimising the Euclidean distance between the unitary orbit of A and C in the general case. Its geometrical aspects, applications and implications are discussed

tosh@crc.dk

Carlsberg Laboratory, Department of Chemistry
Gamle Carlsberg Vej 10
DK-2500 Copenhagen-Valby
Denmark