Tradeoffs for reliable quantum information storage in surface codes and color codes

The family of hyperbolic surface codes is one of the rare families of quantum LDPC codes with non-zero rate and unbounded minimum distance. First, we introduce a family of hyperbolic color codes. This produces a new family of quantum LDPC codes with non-zero rate and with minimum distance logarithmic in the blocklength. Second, we study the tradeoff between the length n, the number of encoded qubits k and the distance d of surface codes and color codes. We prove that kd^2 is upper bounded by C(log k)^2n, where C is a constant that depends only on the row weight of the parity-check matrix. Our results prove that the best asymptotic minimum distance of LDPC surface codes and color codes with non-zero rate is logarithmic in the length.Comment: 10 page

A Construction of Quantum LDPC Codes from Cayley Graphs

We study a construction of Quantum LDPC codes proposed by MacKay, Mitchison and Shokrollahi. It is based on the Cayley graph of Fn together with a set of generators regarded as the columns of the parity-check matrix of a classical code. We give a general lower bound on the minimum distance of the Quantum code in $\mathcal{O}(dn^2)$ where d is the minimum distance of the classical code. When the classical code is the $[n, 1, n]$ repetition code, we are able to compute the exact parameters of the associated Quantum code which are $[[2^n, 2^{\frac{n+1}{2}}, 2^{\frac{n-1}{2}}]]$.Comment: The material in this paper was presented in part at ISIT 2011. This article is published in IEEE Transactions on Information Theory. We point out that the second step of the proof of Proposition VI.2 in the published version (Proposition 25 in the present version and Proposition 18 in the ISIT extended abstract) is not strictly correct. This issue is addressed in the present versio

Efficient color code decoders in d≥2d\geq 2 dimensions from toric code decoders

We introduce an efficient decoder of the color code in $d\geq 2$ dimensions, the Restriction Decoder, which uses any $d$-dimensional toric code decoder combined with a local lifting procedure to find a recovery operation. We prove that the Restriction Decoder successfully corrects errors in the color code if and only if the corresponding toric code decoding succeeds. We also numerically estimate the Restriction Decoder threshold for the color code in two and three dimensions against the bit-filp and phase-flip noise with perfect syndrome extraction. We report that the 2D color code threshold $p_{\textrm{2D}} \approx 10.2\%$ on the square-octagon lattice is on a par with the toric code threshold on the square lattice.Comment: 28 pages, 8 figure

On the Correlation between the Magnetic Activity Levels, the Metallicities and the Radii of Low-Mass Stars

The recent burst in the number of radii measurements of very low-mass stars from eclipsing binaries and interferometry of single stars has opened more questions about what can be causing the discrepancy between the observed radii and the ones predicted by the models. The two main explanations being proposed are a correlation between the radius of the stars and their activity levels or their metallicities. This paper presents a study of such correlations using all the data published to date. The study also investigates correlations between the radii deviation from the models and the masses of the stars. There is no clear correlation between activity level and radii for the single stars in the sample. Those single stars are slow rotators with typical velocities v_rot sini < 3.0 km s^-1. A clear correlation however exists in the case of the faster rotating members of binaries. This result is based on the of X-ray emission levels of the stars. There also appears to be an increase in the deviation of the radii of single stars from the models as a function of metallicity, as previously indicated by Berger et al. (2006). The stars in binaries do not seem to follow the same trend. Finally, the Baraffe et al. (1998) models reproduce well the radius observations below 0.30-0.35Msun, where the stars become fully convective, although this result is preliminary since almost all the sample stars in that mass range are slow rotators and metallicities have not been measured for most of them. The results in this paper indicate that stellar activity and metallicity play an important role on the determination of the radius of very low-mass stars, at least above 0.35Msun.Comment: 22 pages, 4 figures. Accepted for publication on Ap

Discovery of three nearby L dwarfs in the Southern Sky

We report the discovery of three L dwarfs in the solar vicinity within 30 parsecs. These objects were originally found as proper motion objects from a combination of R and I photographic plates measured as part of the SuperCOSMOS Sky Surveys. We subsequently identified these objects as bona fide brown dwarf candidates on the basis of their R-I colour, as first criterion, and subsequently their J-K colours when the infrared data were available from the 2MASS database. Spectroscopic observations in the optical with the ESO 3.6m/EFOSC2 and in the near-infrared with the NTT/SOFI led to the classification of their spectral types as early L dwarfs.Comment: 4 pages including 2 figures, accepted for publication in Astronomy and Astrophysics Letter

Multiepoch Radial Velocity Observations of L Dwarfs

We report on the development of a technique for precise radial-velocity measurements of cool stars and brown dwarfs in the near infrared. Our technique is analogous to the Iodine (I2) absorption cell method that has proven so successful in the optical regime. We rely on telluric CH4 absorption features to serve as a wavelength reference, relative to which we measure Doppler shifts of the CO and H2O features in the spectra of our targets. We apply this technique to high-resolution (R~50,000) spectra near 2.3 micron of nine L dwarfs taken with the Phoenix instrument on Gemini-South and demonstrate a typical precision of 300 m/s. We conduct simulations to estimate our expected precision and show our performance is currently limited by the signal-to-noise of our data. We present estimates of the rotational velocities and systemic velocities of our targets. With our current data, we are sensitive to companions with M sin i > 2MJ in orbits with periods less than three days. We identify no companions in our current data set. Future observations with improved signal-to-noise should result in radial-velocity precision of 100 m/s for L dwarfs.Comment: Accepted for publication in ApJ, 24 pages, 7 figure

Le rôle des institutions culturelles et des missions à Ľ étranger dans la circulation des idées géographiques. Ľ exemple de la carrière de Pierre Deffontaines (1894-1978)

THE PLACE OF CULTURAL POLICY ABROAD IN THE CIRCULATION OF GEOGRAPHICAL IDEAS: THE CASE OF THE CAREER OF PIERRE DEFFONTAINES (1894-1978). Between the two world wars, France reinforced its cultural policy abroad. Many French Institutes were founded, particularly in the coutries of the "Petit Entente" and in Latin America. These institutes were located near foreign universities which helped French Scholars travel abroad. Pierre Deffontaines (1894-1978) is significant in this respect, as most of his carrer took place abroad. Thanks to the two main successive positions which he held - one in France at the Catholic Faculties of Lille (1924-1939), the other in Spain as the director of the French Institute of Barcelona (1939-1964) - he travelled extensively abroad, particularly in the Americas: Brazil, Argentina, Uruguay and Québec. He may have been the French geographer who was the best known abroad and who promoted the largest number of geography departments and associations in various places. As a disciple of Jean Brunhes, he succeeded in associating the promotion of French culture to the promotion of geography