Efficient solvability of Hamiltonians and limits on the power of some quantum computational models

One way to specify a model of quantum computing is to give a set of control Hamiltonians acting on a quantum state space whose initial state and final measurement are specified in terms of the Hamiltonians. We formalize such models and show that they can be simulated classically in a time polynomial in the dimension of the Lie algebra generated by the Hamiltonians and logarithmic in the dimension of the state space. This leads to a definition of Lie-algebraic "generalized mean-field Hamiltonians." We show that they are efficiently (exactly) solvable. Our results generalize the known weakness of fermionic linear optics computation and give conditions on control needed to exploit the full power of quantum computing.     

Probing carbohydrate-lectin recognition in heterogeneous environments with monodisperse cyclodextrin-based glycoclusters

A series of β-cyclodextrin (βCD)-scaffolded glycoclusters exposing heterogeneous yet perfectly controlled displays of α-mannosyl (α-Man) and β-lactosyl (β-Lact) antennas were synthesized to probe the mutual influence of varying densities of the saccharide motifs in the binding properties toward different plant lectins. Enzyme-linked lectin assay (ELLA) data indicated that the presence of β-Lact residues reinforced binding of α-Man to the mannose-specific lectin concanavalin A (Con A) even though homogeneous β-Lact clusters are not recognized at all by this lectin, supporting the existence of synergic recognition mechanisms (heterocluster effect). Conversely, the presence of α-Man motifs in the heteroglycoclusters also resulted in a binding-enhancing effect of β-Lact toward peanut agglutinin (PNA), a lectin strongly binding multivalent lactosides but having no detectable affinity for α-mannopyranosides, for certain architectural arrangements. Two-site, sandwich-type ELLA data corroborated the higher lectin clustering efficiency of heterogeneous glycoclusters compared with homogeneous displays of the putative sugar ligand with identical valency. A turbidity assay was also consistent with the previous observations. Most revealingly, the lectin cross-linking ability of heterogeneous glycoclusters was sensitive to the presence of high concentrations of the non-ligand sugar, strongly suggesting that "mismatching" saccharide motifs may modulate carbohydrate-lectin specific recognition in a lectin-dependent manner when present in highly dense displays together with the "matching" ligand, a situation frequently encountered in biological systems.     

Direct electrochemistry of Phanerochaete chrysosporium cellobiose dehydrogenase covalently attached onto gold nanoparticle modified solid gold electrodes

Achieving efficient electrochemical communication between redox enzymes and various electrode materials is one of the main challenges in bioelectrochemistry and is of great importance for developing electronic applications. Cellobiose dehydrogenase (CDH) is an extracellular flavocytochrome composed of a catalytic FAD containing dehydrogenase domain (DH(CDH)), a heme b containing cytochrome domain (CYT(CDH)), and a flexible linker region connecting the two domains. Efficient direct electron transfer (DET) of CDH from the basidiomycete Phanerochaete chrysosporium (PcCDH) covalently attached to mixed self-assembled monolayer (SAM) modified gold nanoparticle (AuNP) electrode is presented. The thiols used were as follows: 4-aminothiophenol (4-ATP), 4-mercaptobenzoic acid (4-MBA), 4-mercaptophenol (4-MP), 11-mercapto-1-undecanamine (MUNH(2)), 11-mercapto-1-undecanoic acid (MUCOOH), and 11-mercapto-1-undecanol (MUOH). A covalent linkage between PcCDH and 4-ATP or MUNH(2) in the mixed SAMs was formed using glutaraldehyde as cross-linker. The covalent immobilization and the surface coverage of PcCDH were confirmed with surface plasmon resonance (SPR). To improve current density, AuNPs were cast on the top of polycrystalline gold electrodes. For all the immobilized PcCDH modified AuNPs electrodes, cyclic voltammetry exhibited clear electrochemical responses of the CYT(CDH) with fast electron transfer (ET) rates in the absence of substrate (lactose), and the formal potential was evaluated to be +162 mV vs NHE at pH 4.50. The standard ET rate constant (k(s)) was estimated for the first time for CDH and was found to be 52.1, 59.8, 112, and 154 s(-1) for 4-ATP/4-MBA, 4-ATP/4-MP, MUNH(2)/MUCOOH, and MUNH(2)/MUOH modified electrodes, respectively. At all the mixed SAM modified AuNP electrodes, PcCDH showed DET only via the CYT(CDH). No DET communication between the DH(CDH) domain and the electrode was found. The current density for lactose oxidation was remarkably increased by introduction of the AuNPs. The 4-ATP/4-MBA modified AuNPs exhibited a current density up to 30 μA cm(-2), which is ～70 times higher than that obtained for a 4-ATP/4-MBA modified polycrystalline gold electrode. The results provide insight into fundamental electrochemical properties of CDH covalently immobilized on gold electrodes and promote further applications of CDHs for biosensors, biofuel cells, and bioelectrocatalysis.     

A bilayer Double Semion model with symmetry-enriched topological order

We construct a new model of two-dimensional quantum spin systems that combines intrinsic topological orders and a global symmetry called flavour symmetry. It is referred as the bilayer Doubled Semion model (bDS) and is an instance of symmetry-enriched topological order. A honeycomb bilayer lattice is introduced to combine a Double Semion Topological Order with a global spin–flavour symmetry to get the fractionalization of its quasiparticles. The bDS model exhibits non-trivial braiding self-statistics of excitations and its dual model constitutes a Symmetry-Protected Topological Order with novel edge states. This dual model gives rise to a bilayer Non-Trivial Paramagnet that is invariant under the flavour symmetry and the well-known spin flip symmetry.     

Dualities and the phase diagram of the p-clock model

A new “bond-algebraic” approach to duality transformations provides a very powerful technique to analyze elementary excitations in the classical two-dimensional XY and p-clock models. By combining duality and Peierls arguments, we establish the existence of non-Abelian symmetries, the phase structure, and transitions of these models, unveil the nature of their topological excitations, and explicitly show that a continuous U(1) symmetry emerges when p?5. This latter symmetry is associated with the appearance of discrete vortices and Berezinskii-Kosterlitz-Thouless-type transitions. We derive a correlation inequality to prove that the intermediate phase, appearing for p?5, is critical (massless) with decaying power-law correlations.