Fast Decoders for Topological Quantum Codes

We present a family of algorithms, combining real-space renormalization methods and belief propagation, to estimate the free energy of a topologically ordered system in the presence of defects. Such an algorithm is needed to preserve the quantum information stored in the ground space of a topologically ordered system and to decode topological error-correcting codes. For a system of linear size L, our algorithm runs in time log L compared to L^6 needed for the minimum-weight perfect matching algorithm previously used in this context and achieves a higher depolarizing error threshold.Comment: 4 pages, 4 figure

Law School Intentions Of Undergraduate Business Students

The purpose of this paper is to examine factors that influence business students’ intentions to enroll in law school. Scant research has focused on factors that influence business students’ decisions to enroll in law school. This paper attempts to fill that gap. Hypotheses about student intentions are based on Ajzen & Fishbein’s (1977) Theory of Planned Behavior. A sample of students enrolled in a business law class at a large Midwestern university is used to examine the hypotheses. Results indicate that law school intentions are driven by whether students feel they would enjoy the work of a lawyer, whether they feel having a law degree would provide them with job opportunities, and whether they feel they have the skills and abilities to get a law degree. Surprisingly, perceptions about future wealth are not associated with law school intentions. The sample may generalize to business student populations at other large state universities; however, it is important for future researchers to similarly investigate student law school intentions at other types of universities and colleges. The paper encourages undergraduate teachers of business law, as well as administrators of law schools, to consider the determinants of student intentions to study law. We particularly encourage law schools to work with undergraduate law faculty and periodically survey their target undergraduate populations to better understand student perceptions about attending law school

Quantum computing with nearest neighbor interactions and error rates over 1%

Large-scale quantum computation will only be achieved if experimentally implementable quantum error correction procedures are devised that can tolerate experimentally achievable error rates. We describe a quantum error correction procedure that requires only a 2-D square lattice of qubits that can interact with their nearest neighbors, yet can tolerate quantum gate error rates over 1%. The precise maximum tolerable error rate depends on the error model, and we calculate values in the range 1.1--1.4% for various physically reasonable models. Even the lowest value represents the highest threshold error rate calculated to date in a geometrically constrained setting, and a 50% improvement over the previous record.Comment: 4 pages, 8 figure

Maximum weight cycle packing in directed graphs, with application to kidney exchange programs

Centralized matching programs have been established in several countries to organize kidney exchanges between incompatible patient-donor pairs. At the heart of these programs are algorithms to solve kidney exchange problems, which can be modelled as cycle packing problems in a directed graph, involving cycles of length 2, 3, or even longer. Usually, the goal is to maximize the number of transplants, but sometimes the total benefit is maximized by considering the differences between suitable kidneys. These problems correspond to computing cycle packings of maximum size or maximum weight in directed graphs. Here we prove the APX-completeness of the problem of finding a maximum size exchange involving only 2-cycles and 3-cycles. We also present an approximation algorithm and an exact algorithm for the problem of finding a maximum weight exchange involving cycles of bounded length. The exact algorithm has been used to provide optimal solutions to real kidney exchange problems arising from the National Matching Scheme for Paired Donation run by NHS Blood and Transplant, and we describe practical experience based on this collaboration

Glassy states in fermionic systems with strong disorder and interactions

We study the competition between interactions and disorder in two dimensions. Whereas a noninteracting system is always Anderson localized by disorder in two dimensions, a pure system can develop a Mott gap for sufficiently strong interactions. Within a simple model, with short-ranged repulsive interactions, we show that, even in the limit of strong interaction, the Mott gap is completely washed out by disorder for an infinite system for dimensions $D\le 2$. The probability of a nonzero gap falls onto a universal curve, leading to a glassy state for which we provide a scaling function for the frequency dependent susceptibility.Comment: 8 pages, 5 figures, expanded to contain some analytical results for one dimensio

Dynamics of a quantum reference frame undergoing selective measurements and coherent interactions

We consider the dynamics of a quantum directional reference frame undergoing repeated interactions. We first describe how a precise sequence of measurement outcomes affects the reference frame, looking at both the case that the measurement record is averaged over and the case wherein it is retained. We find, in particular, that there is interesting dynamics in the latter situation which cannot be revealed by considering the averaged case. We then consider in detail how a sequence of rotationally invariant unitary interactions affects the reference frame, a situation which leads to quite different dynamics than the case of repeated measurements. We then consider strategies for correcting reference frame drift if we are given a set of particles with polarization opposite to the direction of drift. In particular, we find that by implementing a suitably chosen unitary interaction after every two measurements we can eliminate the rotational drift of the reference frame.Comment: 9 pages, 5 figure

Genome aliquoting with double cut and join

<p>Abstract</p> <p>Background</p> <p>The <it>genome aliquoting probem </it>is, given an observed genome <it>A </it>with <it>n </it>copies of each gene, presumed to descend from an <it>n</it>-way polyploidization event from an ordinary diploid genome <it>B</it>, followed by a history of chromosomal rearrangements, to reconstruct the identity of the original genome <it>B'</it>. The idea is to construct <it>B'</it>, containing exactly one copy of each gene, so as to minimize the number of rearrangements <it>d</it>(<it>A, B' </it>⊕ <it>B' </it>⊕ ... ⊕ <it>B'</it>) necessary to convert the observed genome <it>B' </it>⊕ <it>B' </it>⊕ ... ⊕ <it>B' </it>into <it>A</it>.</p> <p>Results</p> <p>In this paper we make the first attempt to define and solve the genome aliquoting problem. We present a heuristic algorithm for the problem as well the data from our experiments demonstrating its validity.</p> <p>Conclusion</p> <p>The heuristic performs well, consistently giving a non-trivial result. The question as to the existence or non-existence of an exact solution to this problem remains open.</p

Universal topological phase of 2D stabilizer codes

Two topological phases are equivalent if they are connected by a local unitary transformation. In this sense, classifying topological phases amounts to classifying long-range entanglement patterns. We show that all 2D topological stabilizer codes are equivalent to several copies of one universal phase: Kitaev's topological code. Error correction benefits from the corresponding local mappings.Comment: 4 pages, 3 figure

X-ray variability during the quiescent state of the neutron-star X-ray transient in the globular cluster NGC 6440

The globular cluster NGC 6440 is known to harbor a bright neutron-star X-ray transient. We observed the globular cluster with Chandra on two occasions when the bright transient was in its quiescent state in July 2000 and June 2003 (both observations were made nearly 2 years after the end of their preceding outbursts). The quiescent spectrum during the first observation is well represented by a two component model (a neutron-star atmosphere model plus a power-law component which dominates at energies above 2 keV). During the second observation (which was roughly of equal duration to the first observation) we found that the power-law component could no longer be detected. Our spectral fits indicate that the effective temperature of the neutron-star surface was consistent between the two observations. We conclude that the effect of the change in power-law component caused the 0.5-10 keV flux to be a factor of ~2 lower during the second observation compared to the first observation. We discuss plausible explanations for the variations, including variable residual accretion onto the neutron star magnetosphere or some variation in the interaction of the pulsar wind with the matter still outflowing from the companion star.Comment: 18 pages, 3 color figs, 1 b&w figures, 3 tables; discussion expanded; accepted for publication in Ap

Truncated glucagon-like peptide-1 and exendin-4 α-conotoxin pl14a peptide chimeras maintain potency and α-helicity and reveal interactions vital for cAMP signaling in vitro

Glucagon-like peptide-1 (GE P-1) signaling through the glucagon-like peptide 1 receptor (GLP-1R) is a key regulator of normal glucose metabolism, and exogenous GLP-1R agonist therapy is a promising avenue for the treatment of type 2 diabetes mellitus. To date, the development of therapeutic GLP-1R agonists has focused on producing drugs with an extended serum half-life. This has been achieved by engineering synthetic analogs of GLP-1 or the more stable exogenous GLP-1R agonist exendin-4 (Ex-4). These synthetic peptide hormones share the overall structure of GLP-1 and Ex-4, with a C-terminal helical segment and a flexible N-terminal tail. Although numerous studies have investigated the molecular determinants underpinning GLP-1 and Ex-4 binding and signaling through the GLP1R, these have primarily focused on the length and composition of the N-terminal tail or on how to modulate the helicity of the full-length peptides. Here, we investigate the effect of C-terminal truncation in GLP-1 and Ex-4 on the cAMP pathway. To ensure helical C-terminal regions in the truncated peptides, we produced a series of chimeric peptides combining the N-terminal portion of GLP-1 or Ex-4 and the C-terminal segment of the helix-promoting peptide alpha-conotoxin p114a. The helicity and structures of the chimeric peptides were confirmed using circular dichroism and NMR, respectively. We found no direct correlation between the fractional helicity and potency in signaling via the cAMP pathway. Rather, the most important feature for efficient receptor binding and signaling was the C-terminal helical segment (residues 22-27) directing the binding of Phe' into a hydrophobic pocket on the GLP-1R