Quantum Process Tomography of the Quantum Fourier Transform

The results of quantum process tomography on a three-qubit nuclear magnetic resonance quantum information processor are presented, and shown to be consistent with a detailed model of the system-plus-apparatus used for the experiments. The quantum operation studied was the quantum Fourier transform, which is important in several quantum algorithms and poses a rigorous test for the precision of our recently-developed strongly modulating control fields. The results were analyzed in an attempt to decompose the implementation errors into coherent (overall systematic), incoherent (microscopically deterministic), and decoherent (microscopically random) components. This analysis yielded a superoperator consisting of a unitary part that was strongly correlated with the theoretically expected unitary superoperator of the quantum Fourier transform, an overall attenuation consistent with decoherence, and a residual portion that was not completely positive - although complete positivity is required for any quantum operation. By comparison with the results of computer simulations, the lack of complete positivity was shown to be largely a consequence of the incoherent errors during the quantum process tomography procedure. These simulations further showed that coherent, incoherent, and decoherent errors can often be identified by their distinctive effects on the spectrum of the overall superoperator. The gate fidelity of the experimentally determined superoperator was 0.64, while the correlation coefficient between experimentally determined superoperator and the simulated superoperator was 0.79; most of the discrepancies with the simulations could be explained by the cummulative effect of small errors in the single qubit gates.Comment: 26 pages, 17 figures, four tables; in press, Journal of Chemical Physic

Experimental Implementation of the Quantum Baker's Map

This paper reports on the experimental implementation of the quantum baker's map via a three bit nuclear magnetic resonance (NMR) quantum information processor. The experiments tested the sensitivity of the quantum chaotic map to perturbations. In the first experiment, the map was iterated forward and then backwards to provide benchmarks for intrinsic errors and decoherence. In the second set of experiments, the least significant qubit was perturbed in between the iterations to test the sensitivity of the quantum chaotic map to applied perturbations. These experiments are used to investigate previous predicted properties of quantum chaotic dynamics.Comment: submitted to PR

Aircraft and ground-based measurements of hydroperoxides during the 2006 MILAGRO field campaign

International audienceMixing ratios of hydrogen peroxide and hydroxymethyl hydroperoxide were determined aboard the US Department of Energy G-1 Research Aircraft during the March 2006 MILAGRO field campaign in Mexico. Ground measurements of total hydroperoxide were made at the T1 site at Universidad Technologica de Tecámac, about 35 km NW of Mexico City. In the air and on the ground, peroxide mixing ratios near the source region were generally near 1 ppbv, much lower than had been predicted from photochemical models based on the 2003 Mexico City study. Strong southerly flow resulted in transport of pollutants from the T0 to T1 and T2 surface sites on several flight days. On these days, it was observed that peroxide concentrations slightly decreased as the G-1 flew progressively downwind. This observation is consistent with low or negative net peroxide production rates calculated for the source region and is due to the very high NOx concentrations above the Mexico City plateau. However, relatively high values of peroxide were observed at takeoff and landing near Veracruz, a site with much higher humidity and lower NOx concentrations

Dependence of ozone production on NO and hydrocarbons in the troposphere

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95525/1/grl10419.pd

The Edge of Quantum Chaos

We identify a border between regular and chaotic quantum dynamics. The border is characterized by a power law decrease in the overlap between a state evolved under chaotic dynamics and the same state evolved under a slightly perturbed dynamics. For example, the overlap decay for the quantum kicked top is well fitted with $[1+(q-1) (t/\tau)^2]^{1/(1-q)}$ (with the nonextensive entropic index $q$ and $\tau$ depending on perturbation strength) in the region preceding the emergence of quantum interference effects. This region corresponds to the edge of chaos for the classical map from which the quantum chaotic dynamics is derived.Comment: 4 pages, 4 figures, revised version in press PR

A Volumetric Method for Quantifying Atherosclerosis in Mice by Using MicroCT: Comparison to En Face

Precise quantification of atherosclerotic plaque in preclinical models of atherosclerosis requires the volumetric assessment of the lesion(s) while maintaining in situ architecture. Here we use micro-computed tomography (microCT) to detect ex vivo aortic plaque established in three dyslipidemic mouse models of atherosclerosis. All three models lack the low-density lipoprotein receptor (Ldlr−/−), each differing in plaque severity, allowing the evaluation of different plaque volumes using microCT technology. From clearly identified lesions in the thoracic aorta from each model, we were able to determine plaque volume (0.04–3.1 mm3), intimal surface area (0.5–30 mm2), and maximum plaque (intimal-medial) thickness (0.1–0.7 mm). Further, quantification of aortic volume allowed calculation of vessel occlusion by the plaque. To validate microCT for future preclinical studies, we compared microCT data to intimal surface area (by using en face methodology). Both plaque surface area and plaque volume were in excellent correlation between microCT assessment and en face surface area (r2 = 0.99, p<0.0001 and r2 = 0.95, p<0.0001, respectively). MicroCT also identified internal characteristics of the lipid core and fibrous cap, which were confirmed pathologically as Stary type III-V lesions. These data validate the use of microCT technology to provide a more exact empirical measure of ex vivo plaque volume throughout the entire intact aorta in situ for the quantification of atherosclerosis in preclinical models

The time evolution of aerosol composition over the Mexico City plateau

International audienceThe time evolution of aerosol concentration and chemical composition in a megacity urban plume was determined based on 8 flights of the DOE G-1 aircraft in and downwind of Mexico City during the March 2006 MILAGRO field campaign. A series of selection criteria are imposed to eliminate data points with non-urban emission influences. Biomass burning has urban and non-urban sources that are distinguished on the basis of CH3CN and CO. In order to account for dilution in the urban plume, aerosol concentrations are normalized to CO which is taken as an inert tracer of urban emission, proportional to the emissions of aerosol precursors. Time evolution is determined with respect to photochemical age defined as ?Log10 (NOx/NOy). The geographic distribution of photochemical age and CO is examined, confirming the picture that Mexico City is a source region and that pollutants become more dilute and aged as they are advected towards T1 and T2, surface sites that are located at the fringe of the City and 35 km to the NE, respectively. Organic aerosol (OA) per ppm CO is found to increase 7 fold over the range of photochemical ages studied, corresponding to a change in NOx/NOy from nearly 100% to 10%. In the older samples the nitrate/CO ratio has leveled off suggesting that evaporation and formation of aerosol nitrate are in balance. In contrast, OA/CO increases with age in older samples, indicating that OA is still being formed. The amount of carbon equivalent to the deduced change in OA/CO with age is 56 ppbC per ppm CO. At an aerosol yield of 5% and 8% for low and high yield aromatic compounds, it is estimated from surface hydrocarbon observations that only ~9% of the OA formation can be accounted for. A comparison of OA/CO in Mexico City and the eastern U.S. gives no evidence that aerosol yields are higher in a more polluted environment

Chemical Evolution of a Power-Plant Plume

Measurements made from the DOE G-1 aircraft were used to calculate the rate and efficiency of O{sub 3} production downwind of an isolated, coal-fired power plant. The plume was transected 12 times at distances ranging to 65 km from its source (corresponding to an age of {approx}4 h assuming constant wind velocity). For NO{sub x}, a loss rate of 0.5 h{sup -1} was calculated. If reaction with OH was the sole loss mechanism, then an [OH] = 1.6 x 10{sup 7}molec/cm{sup 3} is inferred, which is {approx}2-3X values calculated using a box model constrained by observations. Possible explanations for this discrepancy are discussed. O{sub 3} production per molecule of NO{sub x} approached 6-8 after the plume had aged &gt;3h. Peak O{sub 3} concentrations were 15 ppbv above background. Dilution appears to limit the peak O{sub 3} concentration despite the high production efficiency. Hydrocarbon samples indicate high levels of VOC reactivity ({approx}8 s{sup -1}) in the plume. The number concentration of accumulation mode particles increases significantly with plume age indicating a rapid formation of aerosol mass

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