Solovay-Kitaev Decomposition Strategy for Single-Qubit Channels

Inspired by the Solovay-Kitaev decomposition for approximating unitary operations as a sequence of operations selected from a universal quantum computing gate set, we introduce a method for approximating any single-qubit channel using single-qubit gates and the controlled-NOT (CNOT). Our approach uses the decomposition of the single-qubit channel into a convex combination of "quasiextreme" channels. Previous techniques for simulating general single-qubit channels would require as many as 20 CNOT gates, whereas ours only needs one, bringing it within the range of current experiments

Lanthanum-Mediated Dehydrogenation of 1- and 2-Butynes: Spectroscopy and Formation of La(C\u3csub\u3e4\u3c/sub\u3eH\u3csub\u3e4\u3c/sub\u3e) Isomers

La atom reactions with 1-butyne and 2-butyne are carried out in a laser-vaporization molecular beam source. Both reactions yield the same La-hydrocarbon products from the dehydrogenation and carbon-carbon bond cleavage and coupling of the butynes. The dehydrogenated species La(C4H4) is characterized with mass-analyzed threshold ionization (MATI) spectroscopy and quantum chemical computations. The MATI spectra of La(C4H4) produced from the two reactions exhibit two identical transitions, each consisting of a strong origin band and several vibrational intervals. The two transitions are assigned to the ionization of two isomers: La(η4–CH2CCCH2) (Iso A) and La(η4–CH2CHCCH) (Iso B). The ground electronic states are 2A1 (C2v) for Iso A and 2A (C1) for Iso B. The ionization of the doublet state of each isomer removes a La 6s-based electron and results in a 1A1 ion of Iso A and a 1A ion of Iso B. The formation of Iso A from 2-butyne and Iso B from 1-butyne involves the addition of La to the C≡C triple bond, the activation of two C(sp3)–H bonds, and concerted elimination of a H2 molecule. The formation of Iso A from 1-butyne and Iso B from 2-butyne involves the isomerization of the two butynes to 1,2-butadiene in addition to the concerted H2 elimination

Probing onset of strong localization and electron-electron interactions with the presence of direct insulator-quantum Hall transition

We have performed low-temperature transport measurements on a disordered two-dimensional electron system (2DES). Features of the strong localization leading to the quantum Hall effect are observed after the 2DES undergoes a direct insulator-quantum Hall transition with increasing the perpendicular magnetic field. However, such a transition does not correspond to the onset of strong localization. The temperature dependences of the Hall resistivity and Hall conductivity reveal the importance of the electron-electron interaction effects to the observed transition in our study.Comment: 9 pages, 4 figure

Dependence of the decoherence of polarization states in phase-damping channels on the frequency spectrum envelope of photons

We consider the decoherence of photons suffering in phase-damping channels. By exploring the evolutions of single-photon polarization states and two-photon polarization-entangled states, we find that different frequency spectrum envelopes of photons induce different decoherence processes. A white frequency spectrum can lead the decoherence to an ideal Markovian process. Some color frequency spectrums can induce asymptotical decoherence, while, some other color frequency spectrums can make coherence vanish periodically with variable revival amplitudes. These behaviors result from the non-Markovian effects on the decoherence process, which may give rise to a revival of coherence after complete decoherence.Comment: 7 pages, 4 figures, new results added, replaced by accepted versio

Mass-Analyzed Threshold Ionization Spectroscopy of Lanthanum-Hydrocarbon Radicals Formed by C—H Bond Activation of Propene

La(C3H4) and La(C3H6) are observed from the reaction of laser-vaporized La atoms with propene by photoionization time-of-flight mass spectrometry and characterized by mass-analyzed threshold ionization spectroscopy. Two isomers of La(C3H4) are identified as methyl-lanthanacyclopropene [La(CHCCH3)] (Cs) and lanthanacyclobutene [La(CHCHCH2)] (C1); La(C3H6) is determined to be H—La(η3-allyl) (Cs), a C—H bond inserted species. All three metal-hydrocarbon radicals prefer a doublet ground state with a La 6s-based electron configuration. Ionization of the neutral doublet state of each of these radicals produces a singlet ion state by removing the La-based 6s electron. The threshold ionization allows accurate measurements of the adiabatic ionization energy of the neutral doublet state and metal-ligand and ligand-based vibrational frequencies of the neutral and ionic states. The formation of the three radicals is investigated by density functional theory computations. The inserted species is formed by La inserting into an allylic C—H bond and lanthanacyclopropene by concerted vinylic H2 elimination, whereas lanthanacyclobutene involves both allylic and vinylic dehydrogenations. The inserted species is identified as an intermediate for the formation of lanthanacyclobutene

Spectroscopy and Formation of Lanthanum-Hydrocarbon Radicals Formed by C—C Bond Cleavage and Coupling of Propene

La reaction with propene is carried out in a laser-vaporization molecular beam source. Three La-hydrocarbon radicals are characterized by mass-analyzed threshold ionization (MATI) spectroscopy. One of these radicals is methylenelanthanum [La(CH2)] (Cs), a Schrock-type metal carbene. The other two are a five-membered 1-lanthanacyclopent-3-en [La(CH2CHCHCH2)] (Cs) and a tetrahedron-like trimethylenemethanelanthanum [La(C(CH2)3)] (C3v). Adiabatic ionization energies and metal-ligand stretching and hydrocarbon-based bending frequencies of these species are measured from the MATI spectra, preferred structures and electronic states are identified by comparing the experimental measurements and spectral simulations, and reaction pathways for the formation of the metal-hydrocarbon radicals are investigated with density functional theory calculations. All three radicals prefer doublet ground electronic states with La 6s1-based valence electron configurations, and singly charged cations favor singlet states generated by the removal of the La 6s1 electron. The metal-carbene radical is formed via multi-step carbon-carbon cleavage involving metallacyclization, β-hydrogen migration, and metal insertion. The metal-carbene radical formed in the primary reaction reacts with a second propene molecule to form the five-membered-ring and tetrahedron-like isomers through distinct carbon-carbon coupling paths

Association of DRD4 uVNTR and TP53 codon 72 polymorphisms with schizophrenia: a case-control study

<p>Abstract</p> <p>Background</p> <p>The tumour supressor gene TP53 is thought to be involved in neural apoptosis. The polymorphism at codon 72 in TP53 and the long form variants of the upstream variable number of tandem repeats (uVNTR) polymorphism in the dopamine D4 receptor (DRD4) gene are reported to confer susceptibility to schizophrenia.</p> <p>Methods</p> <p>We recruited 934 patients with schizophrenia and 433 healthy individuals, and genotyped the locus of the TP53 codon 72 and DRD4 uVNTR polymorphisms by combining the polymerase chain reaction-restriction fragment length polymorphism method (PCR-RFLP) with direct sequencing.</p> <p>Results</p> <p>No significant differences were found in the frequency of the genotype of the TP53 codon72 polymorphism between patients with schizophrenia and their controls. However, the long form alleles (≥ 5 repeats) of the DRD4 uVNTR polymorphism were more frequent in patients with schizophrenia than in controls (p = 0.001). Hence, this class of alleles might be a risk factor for enhanced vulnerability to schizophrenia (odds ratio = 3.189, 95% confidence interval = 1.535-6.622). In the logistic regression analysis, the long form variants of the DRD4 polymorphism did predict schizophrenia after the contributions of the age and gender of the subjects were included (p = 0.036, OR = 2.319), but the CC and GG genotypes of the codon 72 polymorphism of TP53 did not.</p> <p>Conclusions</p> <p>The long form variants of the uVNTR polymorphism in DRD4 were associated with schizophrenia, in a manner that was independent of the TP53 codon 72 polymorphism. In addition, given that the genetic effect of the TP53 codon 72 polymorphism on the risk of developing schizophrenia was very small, this polymorphism is unlikely to be associated with schizophrenia. The roles that other single nucleotide polymorphisms (SNPs) in the TP53 gene or in other apoptosis-related genes play in the synaptic dysfunction involved in the pathogenesis of schizophrenia should be investigated.</p