Principles of control for decoherence-free subsystems

Decoherence-free subsystems (DFSs) are a powerful means of protecting quantum information against noise with known symmetry properties. Although Hamiltonians that can implement a universal set of logic gates on DFS encoded qubits without ever leaving the protected subsystem theoretically exist, the natural Hamiltonians that are available in specific implementations do not necessarily have this property. Here we describe some of the principles that can be used in such cases to operate on encoded qubits without losing the protection offered by the DFSs. In particular, we show how dynamical decoupling can be used to control decoherence during the unavoidable excursions outside of the DFS. By means of cumulant expansions, we show how the fidelity of quantum gates implemented by this method on a simple two physical qubit DFS depends on the correlation time of the noise responsible for decoherence. We further show by means of numerical simulations how our previously introduced "strongly modulating pulses" for NMR quantum information processing can permit high-fidelity operations on multiple DFS encoded qubits in practice, provided that the rate at which the system can be modulated is fast compared to the correlation time of the noise. The principles thereby illustrated are expected to be broadly applicable to many implementations of quantum information processors based on DFS encoded qubits.     

One-step purification of a recombinant protein from a whole cell extract by reversed-phase high-performance liquid chromatography

We have developed a one-step facile, flexible and readily scalable purification method for a recombinant protein, TM 1-99 (113 amino acid residues; 12,837 Da) based on reversed-phase high-performance liquid chromatography (RP-HPLC) from an E. coli cell lysate. Following cell lysis, the cell contents were extracted with 0.1% aqueous trifluoroacetic acid (TFA), applied directly under conditions of high sample load to a narrow bore RP-HPLC C(8) column (150 mm x 2.1 mm I.D.) and eluted by a shallow gradient of acetonitrile (0.1%/min). Loads of 23 and 48 mg of lyophilized crude cell extract produced 2.4 and 4.2mg of purified product (>94% pure), respectively, at >94% recovery. Our results show the excellent potential of one-step RP-HPLC for purification of recombinant proteins from cell lysates, where high yields of purified product and greater purity are achieved compared to affinity chromatography. Such an approach was also successful in purifying just trace levels (<0.1% of total contents of crude sample) of TM 1-99 from a cell lysate.     

Dependence of variables construed as an atomic formula

We define a logic D capable of expressing dependence of a variable on designated variables only. Thus D has similar goals to the Henkin quantifiers of [4] and the independence friendly logic of [6] that it much resembles. The logic D achieves these goals by realizing the desired dependence declarations of variables on the level of atomic formulas. By [3] and [17], ability to limit dependence relations between variables leads to existential second order expressive power. Our D avoids some difficulties arising in the original independence friendly logic from coupling the dependence declarations with existential quantifiers. As is the case with independence friendly logic, truth of D is definable inside D. We give such a definition for D in the spirit of [11] and [2] and [1].     

Asymmetric synthesis of pharmaceutically relevant 1-aryl-2-heteroaryl- and 1,2-diheteroarylcyclopropane-1-carboxylates

This study describes general methods for the enantioselective syntheses of pharmaceutically relevant 1-aryl-2-heteroaryl- and 1,2-diheteroarylcyclopropane-1-carboxylates through dirhodium tetracarboxylate-catalysed asymmetric cyclopropanation of vinyl heterocycles with aryl- or heteroaryldiazoacetates. The reactions are highly diastereoselective and high asymmetric induction could be achieved using either (R)-pantolactone as a chiral auxiliary or chiral dirhodium tetracarboxylate catalysts. For meta- or para-substituted aryl- or heteroaryldiazoacetates the optimum catalyst was Rh₂(R-p-Ph-TPCP)₄. In the case of ortho-substituted aryl- or heteroaryldiazoacetates, the optimum catalyst was Rh₂(R-TPPTTL)₄. For a highly enantioselective reaction with the ortho-substituted substrates, 2-chloropyridine was required as an additive in the presence of either 4 Å molecular sieves or 1,1,1,3,3,3-hexafluoroisopropanol (HFIP). Under the optimized conditions, the cyclopropanation could be conducted in the presence of a variety of heterocycles, such as pyridines, pyrazines, quinolines, indoles, oxadiazoles, thiophenes and pyrazoles.

The dirhodium tetracarboxylate-catalysed asymmetric cyclopropanation has been applied to the enantioselective syntheses of pharmaceutically relevant 1-aryl-2-heteroaryl- and 1,2-diheteroarylcyclopropane-1-carboxylates.     

Studies of microwave-enhanced Suzuki-Miyaura vinylation of electron-rich sterically hindered substrates utilizing potassium vinyltrifluoroborate

The Suzuki-Miyaura cross-coupling of sterically hindered and electron-rich ortho,ortho′-substituted aryl halides with potassium vinyltrifluoroborate utilizing microwave irradiation has been conducted while adjusting solvent ratio, irradiation time, and catalyst loading to find optimal conditions. Coupling of benzyl 3,5-bis(benzyloxy)-4-bromobenzoate leads to a mixture of the desired styrene derivative and the reduced product. 4-Bromo-1,3,5-trimethoxybenzene, methyl 4-bromo-3,5-dimethoxybenzoate, and mesitylene bromide were also coupled to test the breadth and scope of this methodology. Of these substrates tested only 4-bromo-1,3,5-trimethoxybenzene was not vinylated successfully, which is believed to be due to the electron-rich nature of this system.     

Anomalous surface diffusion of water compared to aprotic liquids in nanopores

1H nuclear magnetic relaxation dispersion experiments show remarkable differences between water and acetone in contact with microporous glass surfaces containing trace paramagnetic impurities. Analyzed with surface relaxation theory on a model porous system, the data obtained for water show that proton surface diffusion limited by chemical exchange with the bulk phase permits long-range effectively one-dimensional exploration along the pores. This magnetic-field dependence coupled with the anomalous temperature dependence of the relaxation rates permits a direct interpretation in terms of the proton translational diffusion coefficient at the surface of the pores. A universal rescaling applied to these data collected for different pore sizes and on a large variety of frequencies and temperatures, supports this interpretation. The analysis demonstrates that acetone diffuses more slowly, which increases the apparent confinement and results in a two-dimensional model for the molecular dynamics close to surface relaxation sinks. Surface-enhanced water proton diffusion, however, permits the proton to explore a greater spatial extent of the pore, which results in an apparent one-dimensional model for the diffusive motions of the water that dominate nuclear spin relaxation.     

Method validation for determination of alkaloid content in goldenseal root powder

A fast, practical ambient extraction methodology followed by isocratic liquid chromatography (LC) analysis with UV detection was validated for the determination of berberine, hydrastine, and canadine in goldenseal (Hydrastis canadensis L.) root powder. The method was also validated for palmatine, a major alkaloid present in the possible bioadulterants Coptis, Oregon grape root, and barberry bark. Alkaloid standard solutions were linear over the evaluated concentration ranges. The analytical method was linear for alkaloid extraction using 0.3-2 g goldenseal root powder/100 mL extraction solvent. Precision of the method was demonstrated using 10 replicate extractions of 0.5 g goldenseal root powder, with percent relative standard deviation for all 4 alkaloids < or = 1.6. Alkaloid recovery was determined by spiking each alkaloid into triplicate aliquots of neat goldenseal root powder. Recoveries ranged from 92.3% for palmatine to 101.9% for hydrastine. Ruggedness of the method was evaluated by performing multiple analyses of goldenseal root powder from 3 suppliers over a 2-year period. The method was also used to analyze Coptis root, Oregon grape root, barberry bark, and celandine herb, which are possible goldenseal bioadulterants. The resulting chromatographic profiles of the bioadulterants were significantly different from that of goldenseal. The method was directly transferred to LC with mass spectrometry, which was used to confirm the presence of goldenseal alkaloids tetrahydroberberastine, berberastine, canadaline, berberine, hydrastine, and canadine, as well as alkaloids from the bioadulterants, including palmatine, jatrorrhizine, and coptisine.     

A new high frequency “relaxation window” for measuring molecular field fluctuations

We report a new Mössbauer relaxation window which allows the fluctuation rate of a molecular field acting on an impurity in a strongly correlated spin system to be obtained. For a molecular field of 1 T, the fluctuation rate can be measured up to 10 THz, which is three orders of magnitude higher than for the classical relaxation window. The calculated line shapes show that Ising-like fluctuations of the molecular field can be distinguished from other types of fluctuations (in-plane or in space). An application and some other possible uses of this new relaxation window are discussed.