The relationship between minimum gap and success probability in adiabatic quantum computing

We explore the relationship between two figures of merit for an adiabatic quantum computation process: the success probability $P$ and the minimum gap $\Delta_{min}$ between the ground and first excited states, investigating to what extent the success probability for an ensemble of problem Hamiltonians can be fitted by a function of $\Delta_{min}$ and the computation time $T$. We study a generic adiabatic algorithm and show that a rich structure exists in the distribution of $P$ and $\Delta_{min}$. In the case of two qubits, $P$ is to a good approximation a function of $\Delta_{min}$, of the stage in the evolution at which the minimum occurs and of $T$. This structure persists in examples of larger systems.Comment: 13 pages, 6 figures. Substantially updated, with further discussion of the phase diagram and the relation between one- and two-qubit evolution, as well as a greatly extended list of reference

Medicago truncatula contains a second gene encoding a plastid located glutamine synthetase exclusively expressed in developing seeds

<p>Abstract</p> <p>Background</p> <p>Nitrogen is a crucial nutrient that is both essential and rate limiting for plant growth and seed production. Glutamine synthetase (GS), occupies a central position in nitrogen assimilation and recycling, justifying the extensive number of studies that have been dedicated to this enzyme from several plant sources. All plants species studied to date have been reported as containing a single, nuclear gene encoding a plastid located GS isoenzyme per haploid genome. This study reports the existence of a second nuclear gene encoding a plastid located GS in <it>Medicago truncatula</it>.</p> <p>Results</p> <p>This study characterizes a new, second gene encoding a plastid located glutamine synthetase (GS2) in <it>M. truncatula</it>. The gene encodes a functional GS isoenzyme with unique kinetic properties, which is exclusively expressed in developing seeds. Based on molecular data and the assumption of a molecular clock, it is estimated that the gene arose from a duplication event that occurred about 10 My ago, after legume speciation and that duplicated sequences are also present in closely related species of the Vicioide subclade. Expression analysis by RT-PCR and western blot indicate that the gene is exclusively expressed in developing seeds and its expression is related to seed filling, suggesting a specific function of the enzyme associated to legume seed metabolism. Interestingly, the gene was found to be subjected to alternative splicing over the first intron, leading to the formation of two transcripts with similar open reading frames but varying 5' UTR lengths, due to retention of the first intron. To our knowledge, this is the first report of alternative splicing on a plant GS gene.</p> <p>Conclusions</p> <p>This study shows that <it>Medicago truncatula </it>contains an additional GS gene encoding a plastid located isoenzyme, which is functional and exclusively expressed during seed development. Legumes produce protein-rich seeds requiring high amounts of nitrogen, we postulate that this gene duplication represents a functional innovation of plastid located GS related to storage protein accumulation exclusive to legume seed metabolism.</p