The disjointness of stabilizer codes and limitations on fault-tolerant logical gates

Stabilizer codes are a simple and successful class of quantum error-correcting codes. Yet this success comes in spite of some harsh limitations on the ability of these codes to fault-tolerantly compute. Here we introduce a new metric for these codes, the disjointness, which, roughly speaking, is the number of mostly non-overlapping representatives of any given non-trivial logical Pauli operator. We use the disjointness to prove that transversal gates on error-detecting stabilizer codes are necessarily in a finite level of the Clifford hierarchy. We also apply our techniques to topological code families to find similar bounds on the level of the hierarchy attainable by constant depth circuits, regardless of their geometric locality. For instance, we can show that symmetric 2D surface codes cannot have non-local constant depth circuits for non-Clifford gates.Comment: 8+3 pages, 2 figures. Comments welcom

Estimating drizzle drop size and precipitation rate using two-colour lidar measurements

A method to estimate the size and liquid water content of drizzle drops using lidar measurements at two wavelengths is described. The method exploits the differential absorption of infrared light by liquid water at 905 nm and 1.5 μm, which leads to a different backscatter cross section for water drops larger than ≈50 μm. The ratio of backscatter measured from drizzle samples below cloud base at these two wavelengths (the colour ratio) provides a measure of the median volume drop diameter D0. This is a strong effect: for D0=200 μm, a colour ratio of ≈6 dB is predicted. Once D0 is known, the measured backscatter at 905 nm can be used to calculate the liquid water content (LWC) and other moments of the drizzle drop distribution. The method is applied to observations of drizzle falling from stratocumulus and stratus clouds. High resolution (32 s, 36 m) profiles of D0, LWC and precipitation rate R are derived. The main sources of error in the technique are the need to assume a value for the dispersion parameter μ in the drop size spectrum (leading to at most a 35% error in R) and the influence of aerosol returns on the retrieval (≈10% error in R for the cases considered here). Radar reflectivities are also computed from the lidar data, and compared to independent measurements from a colocated cloud radar, offering independent validation of the derived drop size distributions

Core-Collapse Supernova Simulations including Neutrino Interactions from the Virial EOS

Core-collapse supernova explosions are driven by a central engine that converts a small fraction of the gravitational binding energy released during core collapse to outgoing kinetic energy. The suspected mode for this energy conversion is the neutrino mechanism, where a fraction of the neutrinos emitted from the newly formed protoneutron star are absorbed by and heat the matter behind the supernova shock. Accurate neutrino-matter interaction terms are crucial for simulating these explosions. In this proceedings for IAUS 331, SN 1987A, 30 years later, we explore several corrections to the neutrino-nucleon scattering opacity and demonstrate the effect on the dynamics of the core-collapse supernova central engine via two dimensional neutrino-radiation-hydrodynamics simulations. Our results reveal that the explosion properties are sensitive to corrections to the neutral-current scattering cross section at the 10-20% level, but only for densities at or above $\sim 10^{12}$ g cm$^{-3}$Comment: 6 pages, 3 figures, appears in Proc. IAU Symposium 331, SN 1987A, 30 years later - Cosmic Rays and Nuclei from Supernovae and Their Aftermath

STATE-MANDATED FOOD SAFETY CERTIFICATION REQUIREMENTS FOR RESTAURANTS: A 2002 REVIEW OF STATES

The Food and Drug Administration publishes a Standard Food Code which individual states either ratify, or amend and ratify, as the State Food Code. New Jersey has not adopted any revisions to the FDA Standard Food Code since 1993. Currently, the New Jersey Department of Health and Senior Services is considering the implementation of a mandatory food safety certification program for all of the state's foodservice establishments beginning in April 2003. Foodservice businesses serving "high risk" populations, such as the young, ill, or elderly, will be the first segment of the industry required to comply with the new guidelines. Other segments of the industry would be phased in over three years. The exact nature of the revision is yet to be determined; however, it will likely require at least one individual from each foodservice establishment to be certified in proper food safety/food handling techniques. This revision will affect more than 21,000 foodservice businesses that collectively employ 180,000 workers. To proactively respond to the upcoming changes in the State Food Code, the New Jersey Restaurant Association (NJRA) requires information on the status and nature of other state-mandated food safety certification programs. As a service to the foodservice industry, and at the request of the NJRA, the Food Policy Institute at Rutgers University conducted a study to determine the status of state food safety certification requirements across the country. The Institute interviewed all 50 state restaurant associations and found that 16 states presently have some form of state-mandated food safety certification requirement for restaurant workers. Local (municipal or county) food safety certification requirements exist in many states, even in the absence of a state mandate, but these are beyond the scope of this review.Food Consumption/Nutrition/Food Safety,

The Manchester occulting mask imager (MOMI) - first results on the environment of P Cygni

The design and first use of the Manchester occulting mask imager (MOMI) is described. This device, when combined with the Cassegrain or Ritchey-Chretien foci of large telescopes, is dedicated to the imagery of faint line emission regions around bright central sources. Initial observations, with MOMI on the Nordic Optical telescope (NOT), of the V=4.8 mag P~Cygni environment, have revealed a $\geq$~5~arcmin long [NII] 6584A emitting filament projecting from the outer nebular shell of this luminous blue variable (LBV) star. The presence of a mono-polar lobe older than both the inner (22 arcsec diameter) and outer (1.6 arcmin diameter) shells is suggested.Comment: 4 pages, 4 figures, accepted MNRAS 1998 June 1

Comment on ``Can Disorder Induce a Finite Thermal Conductivity in 1D Lattices?''

In a recent paper [Phys. Rev. Lett. 86, 63 (2001)], Li et al have reported that the nonequilibrium heat conducting steady state of a disordered harmonic chain is not unique. In this comment we point out that for a large class of stochastic heat baths the uniqueness of the steady state can be proved, and therefore the findings of Li et al could be either due to their use of deterministic heat baths or insufficient equilibration times in the simulations. We give a simple example where the uniquness of the steady state can be explicitly demonstrated.Comment: 1 page, 1 figure, accepted for publication in Phys. Rev. Let

The Specific Heat of a Ferromagnetic Film.

We analyze the specific heat for the $O(N)$ vector model on a $d$-dimensional film geometry of thickness $L$ using ``environmentally friendly'' renormalization. We consider periodic, Dirichlet and antiperiodic boundary conditions, deriving expressions for the specific heat and an effective specific heat exponent, \alpha\ef. In the case of $d=3$, for $N=1$, by matching to the exact exponent of the two dimensional Ising model we capture the crossover for \xi_L\ra\infty between power law behaviour in the limit {L\over\xi_L}\ra\infty and logarithmic behaviour in the limit {L\over\xi_L}\ra0 for fixed $L$, where $\xi_L$ is the correlation length in the transverse dimensions.Comment: 21 pages of Plain TeX. Postscript figures available upon request from [email protected]