Long-range coupling and scalable architecture for superconducting flux qubits

Constructing a fault-tolerant quantum computer is a daunting task. Given any design, it is possible to determine the maximum error rate of each type of component that can be tolerated while still permitting arbitrarily large-scale quantum computation. It is an underappreciated fact that including an appropriately designed mechanism enabling long-range qubit coupling or transport substantially increases the maximum tolerable error rates of all components. With this thought in mind, we take the superconducting flux qubit coupling mechanism described in PRB 70, 140501 (2004) and extend it to allow approximately 500 MHz coupling of square flux qubits, 50 um a side, at a distance of up to several mm. This mechanism is then used as the basis of two scalable architectures for flux qubits taking into account crosstalk and fault-tolerant considerations such as permitting a universal set of logical gates, parallelism, measurement and initialization, and data mobility.Comment: 8 pages, 11 figure

Thermodynamics and Topology of Disordered Systems: Statistics of the Random Knot Diagrams on Finite Lattice

The statistical properties of random lattice knots, the topology of which is determined by the algebraic topological Jones-Kauffman invariants was studied by analytical and numerical methods. The Kauffman polynomial invariant of a random knot diagram was represented by a partition function of the Potts model with a random configuration of ferro- and antiferromagnetic bonds, which allowed the probability distribution of the random dense knots on a flat square lattice over topological classes to be studied. A topological class is characterized by the highest power of the Kauffman polynomial invariant and interpreted as the free energy of a q-component Potts spin system for q->infinity. It is shown that the highest power of the Kauffman invariant is correlated with the minimum energy of the corresponding Potts spin system. The probability of the lattice knot distribution over topological classes was studied by the method of transfer matrices, depending on the type of local junctions and the size of the flat knot diagram. The obtained results are compared to the probability distribution of the minimum energy of a Potts system with random ferro- and antiferromagnetic bonds.Comment: 37 pages, latex-revtex (new version: misprints removed, references added

Gauge vortex dynamics at finite mass of bosonic fields

The simple derivation of the string equation of motion adopted in the nonrelativistic case is presented, paying the special attention to the effects of finite masses of bosonic fields of an Abelian Higgs model. The role of the finite mass effects in the evaluation of various topological characteristics of the closed strings is discussed. The rate of the dissipationless helicity change is calculated. It is demonstrated how the conservation of the sum of the twisting and writhing numbers of the string is recovered despite the changing helicity.Comment: considerably revised to include errata to journal versio

Influence of a knot on the strength of a polymer strand

Many experiments have been done to determine the relative strength of different knots, and these show that the break in a knotted rope almost invariably occurs at a point just outside the `entrance' to the knot. The influence of knots on the properties of polymers has become of great interest, in part because of their effect on mechanical properties. Knot theory applied to the topology of macromolecules indicates that the simple trefoil or `overhand' knot is likely to be present with high probability in any long polymer strand. Fragments of DNA have been observed to contain such knots in experiments and computer simulations. Here we use {\it ab initio} computational methods to investigate the effect of a trefoil knot on the breaking strength of a polymer strand. We find that the knot weakens the strand significantly, and that, like a knotted rope, it breaks under tension at the entrance to the knot.Comment: 3 pages, 4 figure

On topological interpretation of quantum numbers

It is shown how one can define vector topological charges for topological exitations of non-linear sigma-models on compact homogeneous spaces T_G and G/T_G (where G is a simple compact Lie group and T_G is its maximal commutative subgroup). Explicit solutions for some cases, their energies and interaction of different topological charges are found. A possibility of the topological interpretation of the quantum numbers of groups and particles is discussed.Comment: 20 pages, Latex 2e, modified versio

Heteropolymeric Triplex-Based Genomic Assay® to Detect Pathogens or Single-Nucleotide Polymorphisms in Human Genomic Samples

Human genomic samples are complex and are considered difficult to assay directly without denaturation or PCR amplification. We report the use of a base-specific heteropolymeric triplex, formed by native duplex genomic target and an oligonucleotide third strand probe, to assay for low copy pathogen genomes present in a sample also containing human genomic duplex DNA, or to assay human genomic duplex DNA for Single Nucleotide Polymorphisms (SNP), without PCR amplification. Wild-type and mutant probes are used to identify triplexes containing FVL G1691A, MTHFR C677T and CFTR mutations. The specific triplex structure forms rapidly at room temperature in solution and may be detected without a separation step. YOYO-1, a fluorescent bis-intercalator, promotes and signals the formation of the specific triplex. Genomic duplexes may be assayed homogeneously with single base pair resolution. The specific triple-stranded structures of the assay may approximate homologous recombination intermediates, which various models suggest may form in either the major or minor groove of the duplex. The bases of the stable duplex target are rendered specifically reactive to the bases of the probe because of the activity of intercalated YOYO-1, which is known to decondense duplex locally 1.3 fold. This may approximate the local decondensation effected by recombination proteins such as RecA in vivo. Our assay, while involving triplex formation, is sui generis, as it is not homopurine sequence-dependent, as are “canonical triplexes”. Rather, the base pair-specific heteropolymeric triplex of the assay is conformation-dependent. The highly sensitive diagnostic assay we present allows for the direct detection of base sequence in genomic duplex samples, including those containing human genomic duplex DNA, thereby bypassing the inherent problems and cost associated with conventional PCR based diagnostic assays

Force unfolding kinetics of RNA using optical tweezers. II. Modeling experiments

By exerting mechanical force it is possible to unfold/refold RNA molecules one at a time. In a small range of forces, an RNA molecule can hop between the folded and the unfolded state with force-dependent kinetic rates. Here, we introduce a mesoscopic model to analyze the hopping kinetics of RNA hairpins in an optical tweezers setup. The model includes different elements of the experimental setup (beads, handles and RNA sequence) and limitations of the instrument (time lag of the force-feedback mechanism and finite bandwidth of data acquisition). We investigated the influence of the instrument on the measured hopping rates. Results from the model are in good agreement with the experiments reported in the companion article (1). The comparison between theory and experiments allowed us to infer the values of the intrinsic molecular rates of the RNA hairpin alone and to search for the optimal experimental conditions to do the measurements. We conclude that long handles and soft laser traps represent the best conditions to extract rate estimates that are closest to the intrinsic molecular rates. The methodology and rationale presented here can be applied to other experimental setups and other molecules.Comment: PDF file, 32 pages including 9 figures plus supplementary materia

Numerical study of linear and circular model DNA chains confined in a slit: metric and topological properties

Advanced Monte Carlo simulations are used to study the effect of nano-slit confinement on metric and topological properties of model DNA chains. We consider both linear and circularised chains with contour lengths in the 1.2--4.8 $\mu$m range and slits widths spanning continuously the 50--1250nm range. The metric scaling predicted by de Gennes' blob model is shown to hold for both linear and circularised DNA up to the strongest levels of confinement. More notably, the topological properties of the circularised DNA molecules have two major differences compared to three-dimensional confinement. First, the overall knotting probability is non-monotonic for increasing confinement and can be largely enhanced or suppressed compared to the bulk case by simply varying the slit width. Secondly, the knot population consists of knots that are far simpler than for three-dimensional confinement. The results suggest that nano-slits could be used in nano-fluidic setups to produce DNA rings having simple topologies (including the unknot) or to separate heterogeneous ensembles of DNA rings by knot type.Comment: 12 pages, 10 figure