A General Framework for Recursive Decompositions of Unitary Quantum Evolutions

Decompositions of the unitary group U(n) are useful tools in quantum information theory as they allow one to decompose unitary evolutions into local evolutions and evolutions causing entanglement. Several recursive decompositions have been proposed in the literature to express unitary operators as products of simple operators with properties relevant in entanglement dynamics. In this paper, using the concept of grading of a Lie algebra, we cast these decompositions in a unifying scheme and show how new recursive decompositions can be obtained. In particular, we propose a new recursive decomposition of the unitary operator on $N$ qubits, and we give a numerical example.Comment: 17 pages. To appear in J. Phys. A: Math. Theor. This article replaces our earlier preprint "A Recursive Decomposition of Unitary Operators on N Qubits." The current version provides a general method to generate recursive decompositions of unitary evolutions. Several decompositions obtained before are shown to be as a special case of this general procedur

Grain Filling and Some Fatty Acids Composition of Canola (Brassica napus L.) with Application of Bio-Fertilizers and Irrigation withholding

The effect of irrigation withholding and bio-fertilizers on grain filling components, chlorophyll content and some fatty acids composition Gacomo cultivar of canola, was studied by  factorial experiment based on randomized complete block design with three replications in Agricultural Research Station of Ardabil in 2015-2016. Experimental factors were included irrigation in three levels, full irrigation or control, irrigation withholding at 50% of flowering and pod formation stage, irrigation withholding at 50% of grain formation stage and application of bio fertilizers in four levels, no inoclulation, inoclulation with Nitrobacter, Psedomonas and Azospirillum. Results showed that water limitation decreased yield, number of grain per pod, number of pod per plant, rate and grain filling period, oleic acid, linolenic acid and photosynthetic pigment.­ Whereas erucic acid and palmetic acid content were increased. Means comparison showed that the highest of yield (1.62 ton.ha-1), number of grain per pod (30.66), number of pod per plant (76), grain filling period (54.42 days), chlorophyll a (23.33 mg.g-1 FW), total chlorophyll (29.83 mg.g-1 FW), oleic acid (69.24%) and linolenic acid (11.54%) were obtained in inoculation with Azospirillum and full irrigation. The highest content of erucic acid (2.89 %) and palmetic acid (4.56 %) were observed at no inoculation and irrigation withholding in grain formation stage. Also irrigation withholding in flowering and pod formation stage and grain formation stage decreased 46% and 40.4% respectively from grain yield and application of Azospirillum, Psedomonas and Nitrobacter increased grain yield 53.7%, 9.2% and 44.4% respectively in flowering and pod formation stage and 65.5%, 31% and 17.2% respectively in grain formation stage. According to the results, it seems that Azospirillum application can be suggested as the best treatment for profitable canolaproduction under full irrigation and water limitation condition

Factorizations and Physical Representations

A Hilbert space in M dimensions is shown explicitly to accommodate representations that reflect the prime numbers decomposition of M. Representations that exhibit the factorization of M into two relatively prime numbers: the kq representation (J. Zak, Phys. Today, {\bf 23} (2), 51 (1970)), and related representations termed $q_{1}q_{2}$ representations (together with their conjugates) are analysed, as well as a representation that exhibits the complete factorization of M. In this latter representation each quantum number varies in a subspace that is associated with one of the prime numbers that make up M

Realisation of a programmable two-qubit quantum processor

The universal quantum computer is a device capable of simulating any physical system and represents a major goal for the field of quantum information science. Algorithms performed on such a device are predicted to offer significant gains for some important computational tasks. In the context of quantum information, "universal" refers to the ability to perform arbitrary unitary transformations in the system's computational space. The combination of arbitrary single-quantum-bit (qubit) gates with an entangling two-qubit gate is a gate set capable of achieving universal control of any number of qubits, provided that these gates can be performed repeatedly and between arbitrary pairs of qubits. Although gate sets have been demonstrated in several technologies, they have as yet been tailored toward specific tasks, forming a small subset of all unitary operators. Here we demonstrate a programmable quantum processor that realises arbitrary unitary transformations on two qubits, which are stored in trapped atomic ions. Using quantum state and process tomography, we characterise the fidelity of our implementation for 160 randomly chosen operations. This universal control is equivalent to simulating any pairwise interaction between spin-1/2 systems. A programmable multi-qubit register could form a core component of a large-scale quantum processor, and the methods used here are suitable for such a device.Comment: 7 pages, 4 figure

Pauli Diagonal Channels Constant on Axes

We define and study the properties of channels which are analogous to unital qubit channels in several ways. A full treatment can be given only when the dimension d is a prime power, in which case each of the (d+1) mutually unbiased bases (MUB) defines an axis. Along each axis the channel looks like a depolarizing channel, but the degree of depolarization depends on the axis. When d is not a prime power, some of our results still hold, particularly in the case of channels with one symmetry axis. We describe the convex structure of this class of channels and the subclass of entanglement breaking channels. We find new bound entangled states for d = 3. For these channels, we show that the multiplicativity conjecture for maximal output p-norm holds for p=2. We also find channels with behavior not exhibited by unital qubit channels, including two pairs of orthogonal bases with equal output entropy in the absence of symmetry. This provides new numerical evidence for the additivity of minimal output entropy

Role of 5-lipoxygenase pathway in the pathophysiology of the aortic stenosis

PMID = 2180996

The correlation between Syntax Score and the severity of carotid artery disease

Coronary and carotid artery disease are both known to be specific manifestations of atherosclerosis. The rela­tionship between carotid atherosclerotic disease and coronary artery disease (CAD) has been shown in previous reports. However, the association between complex CAD assessed by the Syntax Score (SxScore) and the severity of carotid arterystenosis (CAS) has not been fully investigated. The objective of this study was to analyze the cor­relation between the severity of CAS and CAD complexity evaluated by SxScore.Materials and Methods: A total of 45 patients with simultaneously carotid and coronary angiography performed were included in our study. SxScore, a marker of CAD complexity, was determined by a special computer soft­ware. The patients were divided into two groups according to the classification of SxScore: low SxScore (n=33, Sx­Score<22) and intermediate-to-high SxScore (n=12, SxScore≥22). The severity of CAS was assessed by digital sub­traction angiography (DSA) of six distinct segments of the carotid artery included the left and right common, in­ternal and external carotid arteries. Spearman`s correlation coefficients were used to determine the correlations between the SxScore and the CAS score.Results: The CAS severity score was significantly higher in patients from the intermediate-to-high SxScore group than in those from the low SxScore group (3/4/4.75 vs. 1/2/3, p=0.001). There was also a significant correlation be­tween the SxScore and the CAS severity score(r=0.47, p=0.001).We revealed that there was a proportional increase in the severity of CAS to CAD complexity using SxScore. It may suggest that complex multivascular atherosclerotic disease is the systemic nature of atherosclerosis

Quercetin both partially attenuates hydrogen peroxide-induced toxicity and decreases viability of rat glial cells

Quercetin is one of the most ubiquitous flavonoids in foods of plant origin. Although quercetin is generally considered to provide protection against oxidative injury, recent studies have shown to be cytotoxic to many cell types. We intended here to determine whether quercetin protects against H2O2-induced toxicity and/or affects viability of rat mixed glial cells. The cells were obtained from 1–3 day olds rat brains and incubated in a humidified atmosphere of 5% CO2, at 37 °C in flasks. In the quercetin groups, different quercetin concentrations (1, 10, 50, 75 or 100 µM) were applied alone for 24 h. For H2O2 cytotoxicity group, the glial cells were treated for 3 h with 100 µM H2O2 which induced 75% cell death. In another group, the cells were treated with 100 µM H2O2 plus respective quercetin concentrations simultaneously for 3 h, the medium was removed and refed for 24 h. MTT test was then applied and statistical significance was ascertained by one way analysis of variance, followed by Tukey’s multiple comparison test. Quercetin starting from 50 µM decreased the glia survival significantly. In H2O2 plus quercetin co-treated groups, both 75 and 100 µM quercetin attenuated toxic effect of H2O2 by 15%. In conclusion, quercetin both partially protects H2O2-induced gliotoxicity and decreases rat glial cell viability in primary culture