Optimal control theory for unitary transformations

The dynamics of a quantum system driven by an external field is well described by a unitary transformation generated by a time dependent Hamiltonian. The inverse problem of finding the field that generates a specific unitary transformation is the subject of study. The unitary transformation which can represent an algorithm in a quantum computation is imposed on a subset of quantum states embedded in a larger Hilbert space. Optimal control theory (OCT) is used to solve the inversion problem irrespective of the initial input state. A unified formalism, based on the Krotov method is developed leading to a new scheme. The schemes are compared for the inversion of a two-qubit Fourier transform using as registers the vibrational levels of the $X^1\Sigma^+_g$ electronic state of Na$_2$. Raman-like transitions through the $A^1\Sigma^+_u$ electronic state induce the transitions. Light fields are found that are able to implement the Fourier transform within a picosecond time scale. Such fields can be obtained by pulse-shaping techniques of a femtosecond pulse. Out of the schemes studied the square modulus scheme converges fastest. A study of the implementation of the $Q$ qubit Fourier transform in the Na$_2$ molecule was carried out for up to 5 qubits. The classical computation effort required to obtain the algorithm with a given fidelity is estimated to scale exponentially with the number of levels. The observed moderate scaling of the pulse intensity with the number of qubits in the transformation is rationalized.Comment: 32 pages, 6 figure

High-Throughput Genetic Mapping of Mutants via Quantitative Single Nucleotide Polymorphism Typing

Advances in next-generation sequencing technology have facilitated the discovery of single nucleotide polymorphisms (SNPs). Sequenom-based SNP-typing assays were developed for 1359 maize SNPs identified via comparative next-generation transcriptomic sequencing. Approximately 75% of these SNPs were successfully converted into genetic markers that can be scored reliably and used to generate a SNP-based genetic map by genotyping recombinant inbred lines from the intermated B73 × Mo17 population. The quantitative nature of Sequenom-based SNP assays led to the development of a time- and cost-efficient strategy to genetically map mutants via quantitative bulked segregant analysis. This strategy was used to rapidly map the loci associated with several dozen recessive mutants. Because a mutant can be mapped using as few as eight multiplexed sets of SNP assays on a bulk of as few as 20 mutant F2 individuals, this strategy is expected to be widely adopted for mapping in many species

Computational comparison between Newtonian and non-Newtonian blood rheologies in stenotic vessels

This work aims at investigating the influence of non-Newtonian blood rheology on the hemodynamics of 3D patient-specific stenotic vessels, by means of a comparison of some numerical results with the Newtonian case. In particular, we consider two carotid arteries with severe stenosis and a stenotic coronary artery treated with a bypass graft, in which we virtually vary the degree of stenosis.We perform unsteady numerical simulations based on the Finite Element method using the Carreau-Yasuda model to describe the non-Newtonian blood rheology. Our results show that velocity, vorticity and wall shear stress distributions are moderately influenced by the non-Newtonian model in case of stenotic carotid arteries. On the other hand, we observed that a non-Newtonian model seems to be important in case of stenotic coronary arteries, in particular to compute the relative residence time which is greatly affected by the rheological model