Bound on quantum computation time: Quantum error correction in a critical environment

We obtain an upper bound on the time available for quantum computation for a given quantum computer and decohering environment with quantum error correction implemented. First, we derive an explicit quantum evolution operator for the logical qubits and show that it has the same form as that for the physical qubits but with a reduced coupling strength to the environment. Using this evolution operator, we find the trace distance between the real and ideal states of the logical qubits in two cases. For a super-Ohmic bath, the trace distance saturates, while for Ohmic or sub-Ohmic baths, there is a finite time before the trace distance exceeds a value set by the user. © 2010 The American Physical Society.

Structural manifestation of the delocalization error of density functional approximations: C(4N+2) rings and C(20) bowl, cage, and ring isomers.

The ground state structure of C(4N+2) rings is believed to exhibit a geometric transition from angle alternation (N < or = 2) to bond alternation (N > 2). All previous density functional theory (DFT) studies on these molecules have failed to reproduce this behavior by predicting either that the transition occurs at too large a ring size, or that the transition leads to a higher symmetry cumulene. Employing the recently proposed perspective of delocalization error within DFT we rationalize this failure of common density functional approximations (DFAs) and present calculations with the rCAM-B3LYP exchange-correlation functional that show an angle-to-bond-alternation transition between C(10) and C(14). The behavior exemplified here manifests itself more generally as the well known tendency of DFAs to bias toward delocalized electron distributions as favored by Huckel aromaticity, of which the C(4N+2) rings provide a quintessential example. Additional examples are the relative energies of the C(20) bowl, cage, and ring isomers; we show that the results from functionals with minimal delocalization error are in good agreement with CCSD(T) results, in contrast to other commonly used DFAs. An unbiased DFT treatment of electron delocalization is a key for reliable prediction of relative stability and hence the structures of complex molecules where many structure stabilization mechanisms exist.

Error recovery in cyberphysical digital microfluidic biochips

Droplet-based digital microfluidics technology has now come of age, and software-controlled biochips for healthcare applications are starting to emerge. However, today's digital microfluidic biochips suffer from the drawback that there is no feedback to the control software from the underlying hardware platform. Due to the lack of precision inherent in biochemical experiments, errors are likely during droplet manipulation; error recovery based on the repetition of experiments leads to wastage of expensive reagents and hard-to-prepare samples. By exploiting recent advances in the integration of optical detectors (sensors) into a digital microfluidics biochip, we present a physical-aware system reconfiguration technique that uses sensor data at intermediate checkpoints to dynamically reconfigure the biochip. A cyberphysical resynthesis technique is used to recompute electrode-actuation sequences, thereby deriving new schedules, module placement, and droplet routing pathways, with minimum impact on the time-to-response. © 2012 IEEE.

Hybrid error correction and de novo assembly of single-molecule sequencing reads.

Single-molecule sequencing instruments can generate multikilobase sequences with the potential to greatly improve genome and transcriptome assembly. However, the error rates of single-molecule reads are high, which has limited their use thus far to resequencing bacteria. To address this limitation, we introduce a correction algorithm and assembly strategy that uses short, high-fidelity sequences to correct the error in single-molecule sequences. We demonstrate the utility of this approach on reads generated by a PacBio RS instrument from phage, prokaryotic and eukaryotic whole genomes, including the previously unsequenced genome of the parrot Melopsittacus undulatus, as well as for RNA-Seq reads of the corn (Zea mays) transcriptome. Our long-read correction achieves >99.9% base-call accuracy, leading to substantially better assemblies than current sequencing strategies: in the best example, the median contig size was quintupled relative to high-coverage, second-generation assemblies. Greater gains are predicted if read lengths continue to increase, including the prospect of single-contig bacterial chromosome assembly.

Long-duration animal tracking in difficult lighting conditions.

High-throughput analysis of animal behavior requires software to analyze videos. Such software typically depends on the experiments' being performed in good lighting conditions, but this ideal is difficult or impossible to achieve for certain classes of experiments. Here, we describe techniques that allow long-duration positional tracking in difficult lighting conditions with strong shadows or recurring "on"/"off" changes in lighting. The latter condition will likely become increasingly common, e.g., for Drosophila due to the advent of red-shifted channel rhodopsins. The techniques enabled tracking with good accuracy in three types of experiments with difficult lighting conditions in our lab. Our technique handling shadows relies on single-animal tracking and on shadows' and flies' being accurately distinguishable by distance to the center of the arena (or a similar geometric rule); the other techniques should be broadly applicable. We implemented the techniques as extensions of the widely-used tracking software Ctrax; however, they are relatively simple, not specific to Drosophila, and could be added to other trackers as well.

The Rational Adolescent: Strategic Information Processing during Decision Making Revealed by Eye Tracking.

Adolescence is often viewed as a time of irrational, risky decision-making - despite adolescents' competence in other cognitive domains. In this study, we examined the strategies used by adolescents (N=30) and young adults (N=47) to resolve complex, multi-outcome economic gambles. Compared to adults, adolescents were more likely to make conservative, loss-minimizing choices consistent with economic models. Eye-tracking data showed that prior to decisions, adolescents acquired more information in a more thorough manner; that is, they engaged in a more analytic processing strategy indicative of trade-offs between decision variables. In contrast, young adults' decisions were more consistent with heuristics that simplified the decision problem, at the expense of analytic precision. Collectively, these results demonstrate a counter-intuitive developmental transition in economic decision making: adolescents' decisions are more consistent with rational-choice models, while young adults more readily engage task-appropriate heuristics.