Scalable and robust randomized benchmarking of quantum processes

In this Letter we propose a fully scalable randomized benchmarking protocol for quantum information processors. We prove that the protocol provides an efficient and reliable estimate of the average error-rate for a set operations (gates) under a very general noise model that allows for both time and gate-dependent errors. In particular we obtain a sequence of fitting models for the observable fidelity decay as a function of a (convergent) perturbative expansion of the gate errors about the mean error. We illustrate the protocol through numerical examples.     

Interfacial polycondensation. I.

Interfacial polycondensation is a rapid, irreversible polymerization at the interface between water containing one difunctional intermediate and an inert immiscible organic solvent containing a complementary difunctional reactant. It is based on the Schotten-Baumann reaction in which acid chlorides are reacted with compounds containing active hydrogen atoms (—OH, —NH and —SH). A large number of polymers (heat-sensitive and infusible as well as stable and meltable) can be prepared. The method has been applied to the preparation of polyurethanes, polyamides, polyureas, polysulfonamides, and polyphenyl esters. Interfacial polycondensations are run in simple, open laboratory equipment with or without stirring. With suitable agitation granular or powdered polymers with high molecular weight are prepared at room temperature and isolated within a few minutes. The intermediates need not be absolutely pure or in balance nor is a quantitative yield needed in order to obtain high polymer. The major variables in the interfacial polycondensation process are discussed and the laboratory techniques and principles are contrasted with melt polycondensation.     

Small-angle X-ray scattering and electron paramagnetic resonance study of the interaction of bovine serum albumin with ionic surfactants

Small-angle X-ray scattering (SAXS) and electron paramagnetic resonance (EPR) techniques have been used to monitor the interaction of bovine serum albumin (BSA) with ionic surfactants such as anionic sodium dodecyl sulfate (SDS), zwitterionic N-hexadecyl-N,N-dimethyl-3-ammonium-1-propane sulfonate (HPS), and cationic cethyltrimethylammonium chloride (CTAC) at pH 7.0. The SAXS results have shown that in the presence of 5 mM SDS and HPS the radius of gyration (Rg) almost does not change as compared to the BSA free-surfactant solution; its value is ca. 30 Angstroms. In the presence of 5 mM CTAC the SAXS data indicate the presence of a particle with a Rg of at least 63 Angstroms, suggesting that in this case, a kind of protein aggregation takes place. In the presence of SDS and HPS surfactants at concentrations above 10 mM, a characteristic broad peak in the region of 0.12-0.18 Angstroms(-1) indicates the presence of micelle-like aggregates in solution. The SAXS curves are consistent with the "pearl necklace" model, where micelle-like aggregates are randomly distributed around the polypeptide chain. EPR results using 5-DSA and 16-DSA spin labels show that in the presence of BSA the EPR spectra are composed of two label populations, one contacting the protein and a second one due to label localization in the micelles. Evidence is also obtained for a competition of the surfactants with the spin labels for the high-affinity binding sites of the stearic acid spin labels as monitored by changes in the fractions of the two label populations as the surfactant concentration is increased. The effect of SDS seems to be stronger in the sense that increased SDS concentration leads to a complete transfer of spin labels from close protein contact sites to micelles, while for HPS, a significant immobilization of probe apparently remains even at higher surfactant concentrations. These two techniques are quite useful since SAXS monitors the overall properties of the scattering particle, while EPR gives information on the dynamics inside this particle and associated with label localization and motion.     

Zur Bestimmung und Trennung des Chroms und zur Analyse von Chrom enthaltenden Substanzen

Ohne Zusammenfassung     

Evaluation of laser level populations of erbium-doped glasses

A simulation of erbium-doped glass systems, which provides population density for the excited states involved in the 1.5 μm and also for 2.7 μm emissions when pumped around 980 nm, is presented. To describe the diode pump laser processes, a theoretical model based in a coupled system of differential rate equations was developed. The approach used and the obtained spectroscopic parameters are discussed. The materials under study are two oxide glasses, lead fluoroborate (PbO-PbF₂-B₂O₃), and heavy metal oxide (Bi₂O₃-PbO-Ga₂O₃) and a fluoride glass (ZrF₄-BaF₂-LaF₃-AlF₃-NaF), all of them doped with Er³⁺.     

Covering properties and Følner conditions for locally compact groups

Summary LetG be a locally compact group with left Haar measurem _G on the Borel sets IB(G) (generated by open subsets) and write |E|=m _G (E). Consider the following geometric conditions on the groupG.(FC If >0 and compact setKG are given, there is a compact setU with 0<|U|< and |x U U|/|U|< for allxK.(A) If >0 and compact setKG, which includes the unit, are given there is a compact setU with 0<|U|< and |K U U|/|U|<.HereA B=(A/B)(B/A) is the symmetric difference set; by regularity ofm _G it makes no difference if we allowU to be a Borel set. It is well known that (A)(FC) and it is known that validity of these conditions is intimately connected with amenability ofG: the existence of a left invariant mean on the spaceCB(G) of all continuous bounded functions. We show, for arbitrary locally compact groupsG, that (amenable)(FC)(A). The proof uses a covering property which may be of interest by itself: we show that every locally compact groupG satisfies.(C) For at least one setK, with int(K)Ø and compact, there is an indexed family {x J}G such that {Kx } is a covering forG whose covering index at each pointg (the number of J withgKx ) is uniformly bounded throughoutG.     

On-line characterisation of apple polyphenols by liquid chromatography coupled with mass spectrometry and ultraviolet absorbance detection

Apple polyphenols were characterised by means of hyphenated techniques such as HPLC coupled to UV photodiode array detection (LC-DAD) and to mass spectrometry (LC-MS). LC-MS using atmospheric pressure ionisation (APCI) in the positive ion mode provided the molecular weight, the number of hydroxyl groups, the number of sugars and an idea about the substitution pattern of the polyphenols. LC-DAD with postcolumn addition of UV shift reagents afforded precise structural information about the position of the free hydroxyl groups in the polyphenolic nucleus. Five isorhamnetin glycosides, two hydroxyphloretin glycosides and quercetin were reported in apple peel for the first time. Postcolumn addition of UV shift reagents in LC-DAD analysis confirmed the presence of isorhamnetin glycosides and not the isomeric glycosides of rhamnetin. Moreover, isorhamnetin-3-O-rhamnoglucoside was identified unambiguously by comparison with a standard. These results are relevant not only from a chemotaxonomic point of view, but also in the control of authenticity of fruit derived products in order to detect fraudulent admixtures.     

Experimental implementation of the quantum baker's map

This Letter reports on the experimental implementation of the quantum baker's map via a three bit nuclear magnetic resonance 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 backward 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 controlled perturbations. These experiments can be used to investigate existing theoretical predictions for quantum chaotic dynamics.