Following a key idea of unconventional geometric quantum computation developed earlier [S. L. Zhu and Z. D. Wang, Phys. Rev. Lett. 91, 187902 (2003)], here we propose a more general scheme in such an intriguing way: γd=αg+ηγg, where γd and γg are respectively the dynamic and geometric phases accumulated in the quantum gate operation, with η as a constant and αg being dependent only on the geometric feature of the operation. More interestingly, we demonstrate an experiment to implement a universal set of such kind of generalized unconventional geometric quantum gates with high fidelity in an NMR system.
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Du et al. (2006) studied this question.