Encoding One Logical Qubit Into Six Physical Qubits

We discuss two methods to encode one qubit into six physical qubits. Each of our two examples corrects an arbitrary single-qubit error. Our first example is a degenerate six-qubit quantum error-correcting code. We explicitly provide the stabilizer generators, encoding circuit, codewords, logical Pauli operators, and logical CNOT operator for this code. We also show how to convert this code into a non-trivial subsystem code that saturates the subsystem Singleton bound. We then prove that a six-qubit code without entanglement assistance cannot simultaneously possess a Calderbank-Shor-Steane (CSS) stabilizer and correct an arbitrary single-qubit error. A corollary of this result is that the Steane seven-qubit code is the smallest single-error correcting CSS code. Our second example is the construction of a non-degenerate six-qubit CSS entanglement-assisted code. This code uses one bit of entanglement (an ebit) shared between the sender and the receiver and corrects an arbitrary single-qubit error. The code we obtain is globally equivalent to the Steane seven-qubit code and thus corrects an arbitrary error on the receiver's half of the ebit as well. We prove that this code is the smallest code with a CSS structure that uses only one ebit and corrects an arbitrary single-qubit error on the sender's side. We discuss the advantages and disadvantages for each of the two codes.Comment: 13 pages, 3 figures, 4 table

A budding yeast model for human disease mutations in the EXOSC2 cap subunit of the RNA exosome complex

RNA exosomopathies, a growing family of diseases, are linked to missense mutations in genes encoding structural subunits of the evolutionarily conserved, 10-subunit exoribonuclease complex, the RNA exosome. This complex consists of a three-subunit cap, a six-subunit, barrel-shaped core, and a catalytic base subunit. While a number of mutations in RNA exosome genes cause pontocerebellar hypoplasia, mutations in the cap subunit gene EXOSC2 cause an apparently distinct clinical presentation that has been defined as a novel syndrome SHRF (short stature, hearing loss, retinitis pigmentosa, and distinctive facies). We generated the first in vivo model of the SHRF pathogenic amino acid substitutions using budding yeast by modeling pathogenic EXOSC2 missense mutations (p.Gly30Val and p.Gly198Asp) in the orthologous S. cerevisiae gene RRP4 The resulting rrp4 mutant cells show defects in cell growth and RNA exosome function. Consistent with altered RNA exosome function, we detect significant transcriptomic changes in both coding and noncoding RNAs in rrp4-G226D cells that model EXOSC2 p.Gly198Asp, suggesting defects in nuclear surveillance. Biochemical and genetic analyses suggest that the Rrp4 G226D variant subunit shows impaired interactions with key RNA exosome cofactors that modulate the function of the complex. These results provide the first in vivo evidence that pathogenic missense mutations present in EXOSC2 impair the function of the RNA exosome. This study also sets the stage to compare exosomopathy models to understand how defects in RNA exosome function underlie distinct pathologies

Observation of the radiative decay mode of the free neutron

The theory of quantum electrodynamics (QED) predicts that beta decay of the neutron into a proton, electron and antineutrino should be accompanied by a continuous spectrum of soft photons. While this inner bremsstrahlung branch has been previously measured in nuclear beta and electron capture decay, it has never been observed in free neutron decay. Recently, the photon energy spectrum and branching ratio for neutron radiative decay have been calculated using two approaches: a standard QED framework(1-3) and heavy baryon chiral perturbation theory(4) (an effective theory of hadrons based on the symmetries of quantum chromodynamics). The QED calculation treats the nucleons as point-like, whereas the latter approach includes the effect of nucleon structure in a systematic way. Here we observe the radiative decay mode of free neutrons, measuring photons in coincidence with both the emitted electron and proton. We determined a branching ratio of (3.13 +/- 0.34) x 10(-3) (68 per cent level of confidence) in the energy region between 15 and 340 keV, where the uncertainty is dominated by systematic effects. The value is consistent with the predictions of both theoretical approaches; the characteristic energy spectrum of the radiated photons, which differs from the uncorrelated background spectrum, is also consistent with the calculated spectrum. This result may provide opportunities for more detailed investigations of the weak interaction processes involved in neutron beta decay.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62639/1/nature05390.pd

Assessing the relationship between chromatin and splicing factors in alternative splicing

Proteins that bind to DNA or RNA are both known to influence alternative splicing. However, there has not been so far a systematic experimental exploration of the relationship between these factors in their effect on splicing. In this thesis, we make use of the large amounts of publicly available high throughput sequencing data that now make it possible to explore this question on a genome-wide scale. We made exhaustive use of a method known as profiling to address this question. As most profiling methods in common use are merely qualitative, the first task of the thesis was to generate a quantitative profiling method and bioinformatics tool, ProfileSeq, which we validated by reproducing previous results from the literature. ProfileSeq and other methods were combined to mine for relationships between DNA and RNA binding factors with potential relevance to splicing. We found significant associations between the transcription factor CTCF and the RNA binding protein LIN28A, and similarly between SPI1 and RNA-binding proteins that bind to AC-rich motifs, such as hnRNPL. These represent putative relationships relevant to splicing, as these results were reached by more than one independent method with independent datasets. We also show evidence that CTCF acts as a barrier between regions of H3K4me3 marking inside genes. A number of other results of potential interest to both the bioinformatics and molecular biology communities are also describedLas proteínas que se unen al DNA o al RNA pueden influir el splicing alternativo. Sin embargo, no ha habido aún una exploración sistemática de la relación entre estos dos tipos de factores en su acción sobre el splicing. En esta tesis hacemos uso de datos públicos de secuenciación de alto rendimiento para explorar esta cuestión a escala de todo el genoma. Hemos hecho un uso sistemático de la construcción de perfiles de información genómica para abordar esta cuestión. Debido a que los métodos i comúnmente utilizados para construir perfiles hace sólo comparaciones cualitativas, la primera tarea de esta tesis consistió en desarrollar un método para cuantificar perfiles e implementarlo en una herramienta bioinformática, ProfileSeq, la cual hemos validado mediante la reproducción de resultados previamente descritos en la literatura. Posteriormente, ProfileSeq se usó con datos de actividad de unión al DNA o al RNA de distintas proteínas para estudiar la relevancia en el splicing. Se encontraron varias asociaciones significativas. Entre ellas, la del factor de transcripción CTCF y la proteína de unión a RNA LIN28A. De manera similar, se encontró una relación entre SPI1 y proteínas de unión a RNA que se unen a motivos ricos en AC, como hnRNPL. Estos resultados representan relaciones putativas relevantes para el splicing, ya que se alcanzaron por más de un método diferente y usando datos independientes, También mostramos evidencia de que CTCF actúa como una barrera entre las regiones intragénicas de marcaje diferencial con H3K4me3. También se describen otros resultados de interés potencial tanto para la bioinformática como para la biología molecular

Dance spirit

<p>(A) Mappability according to transcript length. “Longest” gives the longest 20% of transcript lengths, “long” gives the 2^nd longest 20% of transcript lengths, and so on. Each class has N = 11711 reference regions. (B) Mappability at the upper vs. lower quartile of splice site strengths, “strong” and “weak”, respectively. (C)-(E) Comparisons of regions surrounding transcription start sites (TSSs) and polyadenylation sites (pA-sites). The pA profiles have been inverted, such that for all these profiles, positive values on the x-axis indicate the distance into the transcript, whereas negative values indicate the distance outside of the transcript. (F)-(G) Mouse CLIP-Seq profiles at strong vs. weak exons. Test vs. control P-values/bin are as shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0132448#pone.0132448.g001" target="_blank">Fig 1B</a>, with the lightest shade of grey corresponding to P-value < 0.01.</p

Contingency matrix for genome-wide ChIA-PET and ChIP-Seq overlaps.

<p>Contingency matrix for genome-wide ChIA-PET and ChIP-Seq overlaps.</p

Workflow of ProfileSeq.

<p>Rectangles indicate files. Arrows leaving from files indicate outputs; arrows coming into a file indicate inputs. The user first prepares Test and Control reference files (.ref) containing the positions at which the datasets are to be plotted, as well as a BED or.pos file with the data to plot (A). The.ref and.pos formats are as displayed, except that the id field required for the.ref format is not shown. The BED or.pos file must be pre-processed such that the maximum number of times a read can be repeated at a given coordinate (chromosome position strand) is known. An optional file of genomic coordinates of mappable reads or input reads may be used for more accurate results. Each pair of.ref and BED/.pos files are then input into <i>count_occurences</i>, which will output a file of the counts of occurrences (.occ) of reads in the BED/.pos file at and around the positions in the.ref file (B). The.occ files are then used as inputs to ProfileSeq, which generates a profile like the one shown, as well as files with a list of significant regions and P-values of Test vs. Control counts in each bin. Additionally, using <i>ProfileSeq_peaks</i>, the count of occurrences in the central region c is compared to the counts in the immediately flanking regions (a and b) on the Test and Control profiles separately. Software and usage details are available at <a href="https://bitbucket.org/regulatorygenomicsupf/profileseq/" target="_blank">https://bitbucket.org/regulatorygenomicsupf/profileseq/</a>.</p

Contingency matrix for P-value calculations in ProfileSeq.

<p>Contingency matrix for P-value calculations in ProfileSeq.</p

Comparison of internal exons with or without peaks nearby.

<p>US = peak center within 1kb upstream of 3'SS. DS = peak center within 1kb downstream of 5'SS. Pu1 = SPI1/PU.1 gene. (A) Splice site strengths of internal exons with or without transcription factor peaks nearby. P-values below each plot are based on the Wilcoxon test. Only exons longer than 100nt are considered. (B)-(C) RBP motif profiles at exons with or without peaks nearby. “Strong” and “weak” are the upper and lower 50% of splice site strengths, respectively. Only exons longer than 103nt are considered. Test and control exon sets for all profiles shown are matched for exon length, GC-content, and SS strength. Test vs. control P-values/bin are as shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0132448#pone.0132448.g001" target="_blank">Fig 1B</a>, with the lightest shade of grey corresponding to P-value < 0.01.</p

Contingency matrix for ChIA-PET/ChIP-Seq overlaps involving a TSS.

<p>Contingency matrix for ChIA-PET/ChIP-Seq overlaps involving a TSS.</p