Bound on quantum computation time: Quantum error correction in a critical environment

We obtain an upper bound on the time available for quantum computation for a given quantum computer and decohering environment with quantum error correction implemented. First, we derive an explicit quantum evolution operator for the logical qubits and show that it has the same form as that for the physical qubits but with a reduced coupling strength to the environment. Using this evolution operator, we find the trace distance between the real and ideal states of the logical qubits in two cases. For a super-Ohmic bath, the trace distance saturates, while for Ohmic or sub-Ohmic baths, there is a finite time before the trace distance exceeds a value set by the user. © 2010 The American Physical Society.

Refractive changes after descemet stripping endothelial keratoplasty: a simplified mathematical model.

PURPOSE: To develop a mathematical model that can predict refractive changes after Descemet stripping endothelial keratoplasty (DSEK). METHODS: A mathematical formula based on the Gullstrand eye model was generated to estimate the change in refractive power of the eye after DSEK. This model was applied to four DSEK cases retrospectively, to compare measured and predicted refractive changes after DSEK. RESULTS: The refractive change after DSEK is determined by calculating the difference in the power of the eye before and after DSEK surgery. The power of the eye post-DSEK surgery can be calculated with modified Gullstrand eye model equations that incorporate the change in the posterior radius of curvature and change in the distance between the principal planes of the cornea and lens after DSEK. Analysis of this model suggests that the ratio of central to peripheral graft thickness (CP ratio) and central thickness can have significant effect on refractive change where smaller CP ratios and larger graft thicknesses result in larger hyperopic shifts. This model was applied to four patients, and the average predicted hyperopic shift in the overall power of the eye was calculated to be 0.83 D. This change reflected in a mean of 93% (range, 75%-110%) of patients' measured refractive shifts. CONCLUSIONS: This simplified DSEK mathematical model can be used as a first step for estimating the hyperopic shift after DSEK. Further studies are necessary to refine the validity of this model.

Chromosomal organization of adrenergic receptor genes.

The adrenergic receptors (ARs) (subtypes alpha 1, alpha 2, beta 1, and beta 2) are a prototypic family of guanine nucleotide binding regulatory protein-coupled receptors that mediate the physiological effects of the hormone epinephrine and the neurotransmitter norepinephrine. We have previously assigned the genes for beta 2- and alpha 2-AR to human chromosomes 5 and 10, respectively. By Southern analysis of somatic cell hybrids and in situ chromosomal hybridization, we have now mapped the alpha 1-AR gene to chromosome 5q32----q34, the same position as beta 2-AR, and the beta 1-AR gene to chromosome 10q24----q26, the region where alpha 2-AR is located. In mouse, both alpha 2- and beta 1-AR genes were assigned to chromosome 19, and the alpha 1-AR locus was localized to chromosome 11. Pulsed field gel electrophoresis has shown that the alpha 1- and beta 2-AR genes in humans are within 300 kilobases (kb) and the distance between the alpha 2- and beta 1-AR genes is less than 225 kb. The proximity of these two pairs of AR genes and the sequence similarity that exists among all the ARs strongly suggest that they are evolutionarily related. Moreover, they likely arose from a common ancestral receptor gene and subsequently diverged through gene duplication and chromosomal duplication to perform their distinctive roles in mediating the physiological effects of catecholamines. The AR genes thus provide a paradigm for understanding the evolution of such structurally conserved yet functionally divergent families of receptor molecules.