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

Qcmpi: A Parallel Environment for Quantum Computing

QCMPI is a quantum computer (QC) simulation package written in Fortran 90 with parallel processing capabilities. It is an accessible research tool that permits rapid evaluation of quantum algorithms for a large number of qubits and for various "noise" scenarios. The prime motivation for developing QCMPI is to facilitate numerical examination of not only how QC algorithms work, but also to include noise, decoherence, and attenuation effects and to evaluate the efficacy of error correction schemes. The present work builds on an earlier Mathematica code QDENSITY, which is mainly a pedagogic tool. In QCMPI, the stress is on state vectors, in order to employ a large number of qubits. The parallel processing feature is implemented by using the Message-Passing Interface (MPI) protocol. Codes for Grover's search and Shor's factoring algorithms are provided as examples. A major feature of this work is that concurrent versions of the algorithms can be evaluated with each version subject to alternate noise effects, which corresponds to the idea of solving a stochastic Schr\"{o}dinger equation.Comment: Package webpage http://www.pitt.edu/~tabakin/QCMP

Radiative β decay of the free neutron

The theory of quantum electrodynamics predicts that the β decay of the neutron into a proton, electron, and antineutrino is accompanied by a continuous spectrum of emitted photons described as inner bremsstrahlung. While this phenomenon has been observed in nuclear β decay and electron-capture decay for many years, it has only been recently observed in free-neutron decay. We present a detailed discussion of an experiment in which the radiative decay mode of the free neutron was observed. In this experiment, the branching ratio for this rare decay was determined by recording photons that were correlated with both the electron and proton emitted in neutron decay. We determined the branching ratio for photons with energy between 15 and 340 keV to be (3.09±0.32)×10-3 (68% level of confidence), where the uncertainty is dominated by systematic effects. This value for the branching ratio is consistent with theoretical predictions. The characteristic energy spectrum of the radiated photons, which differs from the uncorrelated background spectrum, is also consistent with the theoretical spectrum

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

Quantum Convolutional Coding with Shared Entanglement: General Structure

We present a general theory of entanglement-assisted quantum convolutional coding. The codes have a convolutional or memory structure, they assume that the sender and receiver share noiseless entanglement prior to quantum communication, and they are not restricted to possess the Calderbank-Shor-Steane structure as in previous work. We provide two significant advances for quantum convolutional coding theory. We first show how to "expand" a given set of quantum convolutional generators. This expansion step acts as a preprocessor for a polynomial symplectic Gram-Schmidt orthogonalization procedure that simplifies the commutation relations of the expanded generators to be the same as those of entangled Bell states (ebits) and ancilla qubits. The above two steps produce a set of generators with equivalent error-correcting properties to those of the original generators. We then demonstrate how to perform online encoding and decoding for a stream of information qubits, halves of ebits, and ancilla qubits. The upshot of our theory is that the quantum code designer can engineer quantum convolutional codes with desirable error-correcting properties without having to worry about the commutation relations of these generators.Comment: 23 pages, replaced with final published versio

DNA Sensors with Diamond as a Promising Alternative Transducer Material

Bio-electronics is a scientific field coupling the achievements in biology with electronics to obtain higher sensitivity, specificity and speed. Biosensors have played a pivotal role, and many have become established in the clinical and scientific world. They need to be sensitive, specific, fast and cheap. Electrochemical biosensors are most frequently cited in literature, often in the context of DNA sensing and mutation analysis. However, many popular electrochemical transduction materials, such as silicon, are susceptible to hydrolysis, leading to loss of bioreceptor molecules from the surface. Hence, increased attention has been shifted towards diamond, which surpasses silicon on many levels

Highly parallel oligonucleotide purification and functionalization using reversible chemistry

We have developed a cost-effective, highly parallel method for purification and functionalization of 5′-labeled oligonucleotides. The approach is based on 5′-hexa-His phase tag purification, followed by exchange of the hexa-His tag for a functional group using reversible reaction chemistry. These methods are suitable for large-scale (micromole to millimole) production of oligonucleotides and are amenable to highly parallel processing of many oligonucleotides individually or in high complexity pools. Examples of the preparation of 5′-biotin, 95-mer, oligonucleotide pools of >40K complexity at micromole scale are shown. These pools are prepared in up to ~16% yield and 90–99% purity. Approaches for using this method in other applications are also discussed

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

Poly(ADP-ribosyl)ation associated changes in CTCF-chromatin binding and gene expression in breast cells

CTCF is an evolutionarily conserved and ubiquitously expressed architectural protein regulating a plethora of cellular functions via different molecular mechanisms. CTCF can undergo a number of post-translational modifications which change its properties and functions. One such modifications linked to cancer is poly(ADP-ribosyl)ation (PARylation). The highly PARylated CTCF form has an apparent molecular mass of 180 kDa (referred to as CTCF180), which can be distinguished from hypo- and non-PARylated CTCF with the apparent molecular mass of 130 kDa (referred to as CTCF130). The existing data accumulated so far have been mainly related to CTCF130. However, the properties of CTCF180 are not well understood despite its abundance in a number of primary tissues. In this study we performed ChIP-seq and RNA-seq analyses in human breast cells 226LDM, which display predominantly CTCF130 when proliferating, but CTCF180 upon cell cycle arrest. We observed that in the arrested cells the majority of sites lost CTCF, whereas fewer sites gained CTCF or remain bound (i.e. common sites). The classical CTCF binding motif was found in the lost and common, but not in the gained sites. The changes in CTCF occupancies in the lost and common sites were associated with increased chromatin densities and altered expression from the neighboring genes. Based on these results we propose a model integrating the CTCF130/180 transition with CTCF-DNA binding and gene expression changes. This study also issues an important cautionary note concerning the design and interpretation of any experiments using cells and tissues where CTCF180 may be present

Understanding 'non-genetic' inheritance : insights from molecular-evolutionary crosstalk

The idea for this paper was initially proposed by I.A.-K. and was further developed by all authors in a workshop generously funded by grant No 789240 from the European Research Council (ERC) to F.J.W. S.E.S. acknowledges support from Wesleyan University and The John Templeton Foundation.Understanding the evolutionary and ecological roles of 'non-genetic' inheritance (NGI) is daunting due to the complexity and diversity of epigenetic mechanisms. We draw on insights from molecular and evolutionary biology perspectives to identify three general features of 'non-genetic' inheritance systems: (i) they are functionally interdependent with, rather than separate from, DNA sequence; (ii) precise mechanisms vary phylogenetically and operationally; and (iii) epigenetic elements are probabilistic, interactive regulatory factors and not deterministic 'epialleles' with defined genomic locations and effects. We discuss each of these features and offer recommendations for future empirical and theoretical research that implements a unifying inherited gene regulation (IGR) approach to studies of 'non-genetic' inheritance.Publisher PDFPeer reviewe