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

Theory of Quantum Optical Control of Single Spin in a Quantum Dot

We present a theory of quantum optical control of an electron spin in a single semiconductor quantum dot via spin-flip Raman transitions. We show how an arbitrary spin rotation may be achieved by virtual excitation of discrete or continuum trion states. The basic physics issues of the appropriate adiabatic optical pulses in a static magnetic field to perform the single qubit operation are addressed

The role of human CYP2C8 and CYP2C9 variants in pioglitazone metabolism in vitro

The cytochrome P450 enzyme CYP2C8 appears to have a major role in pioglitazone metabolism. The present study was conducted to further clarify the role of individual CYPs and of the CYP2C8/9 polymorphisms in the primary metabolism of pioglitazone in vitro. Pioglitazone (2-400 microM) was incubated with isolated cytochrome P450 enzymes or human liver microsomes, some of them carrying either the CYP2C8*3/*3 genotype (and also the CYP2C9*2/*2 genotype) or the CYP2C8*1/*1 genotype (five samples each). The formation of the primary pioglitazone metabolite M-IV was monitored by HPLC. Enzyme kinetics were estimated assuming a single binding site. Mean intrinsic clearance of pioglitazone to the metabolite M-IV was highest for CYP2C8 and CYP1A2 with 58 pmol M-IV/min/nmol CYP P450/microM pioglitazone each, 53 for CYP2D6*1, 40 for CYP2C19*1, and 34 for CYP2C9*2, respectively. CYP2A6, CYP2B6, CYP2C9*1, CYP2C9*3, CYP2E1, CYP3A4 and CYP3A5 did not form quantifiable amounts of M-IV. CYP2C8*1/*1 microsomes (25 +/- 4 pmol M-IV/min/mg protein/muM pioglitazone) showed lower intrinsic clearance of pioglitazone than CYP2C8*3/*3 microsomes (35 +/- 9, p = 0.04). In all samples, metabolite formation showed substrate inhibition, while pioglitazone did not inhibit CYP2C8-mediated paclitaxel metabolism. CYP2C8, CYP1A2 and CYP2D6 are major CYPs forming M-IV in vitro. The higher activity of CYP2C8*3/CYP2C9*2 microsomes may result from a contribution of CYP2C9*2, or from differences in CYP2C8 expression. The evidence for substrate-specific inhibitory effects of pioglitazone on CYP2C-mediated metabolism needs to be tested in further studies

Rhinomanometric reference intervals for normal total nasal airflow resistance

Background: Reference intervals (Rls) or mean values for normal total nasal airflow resistance are essential for the diagnosis of nasal obstruction. Data relating to nasal airflow are not standardised, and valid and reliable Rls do not exist for the time being. This meta-analysis aimed to determine such standard95%-Rls. Methodology: Research of related literature listed in Medline, Embase, Cochrane, and Web of Science databases. Results: Airflow resistance data were gathered from 38 studies using active anterior rhinomanometry at a differential pressure of 150Pa to examine patients under congested and decongested mucosal conditions. In the meta-analysis overall values and Rls for normal total nasal airflow resistance under congested nasal mucosal conditions were calculated for all subjects at 0.25Pa/ cm(3)/s (95%-RI 0.10-0.40Pa/cm(3)/s), adults regardless of gender at 0.25Pa/cm(3)/s (95%-RI 0.12-0.38Pa/cm(3)/s), men at 0.24Pa/cm(3)/s (95%-RI 0.09-0.39Pa/cm(3)/s), and women at 0.26Pa/cm(3)/s (95%-RI 0.08-0.44Pa/cm(3)/s). Asian, African and Caucasian ethnic groups exhibited rising airflow resistance mean values: 0.23Pa/cm(3)/s (95%-RI 0.08-0.39Pa/cm(3)/s), 0.25Pa/cm(3)/s (95%-RI 0.11-0.38Pa/cm(3)/s) and 0.26Pa/cm(3)/s (95%-RI 0.13-0.38Pa/cm(3)/s), respectively. Lower overall mean values resulted under decongested nasal mucosal conditions. Conclusion:The reference intervals and mean values ascertained in this meta-analysis improve the diagnosis of nasal obstruction and may represent a useful supplement in existing guidelines for the standardisation of rhinomanometric measurements

Broadband similariton : applications to ultrafast optics and photonics

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