Improved Simulation of Stabilizer Circuits

The Gottesman-Knill theorem says that a stabilizer circuit -- that is, a quantum circuit consisting solely of CNOT, Hadamard, and phase gates -- can be simulated efficiently on a classical computer. This paper improves that theorem in several directions. First, by removing the need for Gaussian elimination, we make the simulation algorithm much faster at the cost of a factor-2 increase in the number of bits needed to represent a state. We have implemented the improved algorithm in a freely-available program called CHP (CNOT-Hadamard-Phase), which can handle thousands of qubits easily. Second, we show that the problem of simulating stabilizer circuits is complete for the classical complexity class ParityL, which means that stabilizer circuits are probably not even universal for classical computation. Third, we give efficient algorithms for computing the inner product between two stabilizer states, putting any n-qubit stabilizer circuit into a "canonical form" that requires at most O(n^2/log n) gates, and other useful tasks. Fourth, we extend our simulation algorithm to circuits acting on mixed states, circuits containing a limited number of non-stabilizer gates, and circuits acting on general tensor-product initial states but containing only a limited number of measurements.Comment: 15 pages. Final version with some minor updates and corrections. Software at http://www.scottaaronson.com/ch

Large scale cosmic-ray anisotropy with KASCADE

The results of an analysis of the large scale anisotropy of cosmic rays in the PeV range are presented. The Rayleigh formalism is applied to the right ascension distribution of extensive air showers measured by the KASCADE experiment.The data set contains about 10^8 extensive air showers in the energy range from 0.7 to 6 PeV. No hints for anisotropy are visible in the right ascension distributions in this energy range. This accounts for all showers as well as for subsets containing showers induced by predominantly light respectively heavy primary particles. Upper flux limits for Rayleigh amplitudes are determined to be between 10^-3 at 0.7 PeV and 10^-2 at 6 PeV primary energy.Comment: accepted by The Astrophysical Journa

Primary Proton Spectrum of Cosmic Rays measured with Single Hadrons

The flux of cosmic-ray induced single hadrons near sea level has been measured with the large hadron calorimeter of the KASCADE experiment. The measurement corroborates former results obtained with detectors of smaller size if the enlarged veto of the 304 m^2 calorimeter surface is encounted for. The program CORSIKA/QGSJET is used to compute the cosmic-ray flux above the atmosphere. Between E_0=300 GeV and 1 PeV the primary proton spectrum can be described with a power law parametrized as dJ/dE_0=(0.15+-0.03)*E_0^{-2.78+-0.03} m^-2 s^-1 sr^-1 TeV^-1. In the TeV region the proton flux compares well with the results from recent measurements of direct experiments.Comment: 13 pages, accepted by Astrophysical Journa

KASCADE: Astrophysical results and tests of hadronic interaction models

KASCADE is a multi-detector setup to get redundant information on single air shower basis. The information is used to perform multiparameter analyses to solve the threefold problem of the reconstruction of (i)the unknown primary energy, (ii) the primary mass, and (iii) to quantify the characteristics of the hadronic interactions in the air-shower development. In this talk recent results of the KASCADE data analyses are summarized concerning cosmic ray anisotropy studies, determination of flux spectra for different primary mass groups, and approaches to test hadronic interaction models. Neither large scale anisotropies nor point sources were found in the KASCADE data set. The energy spectra of the light element groups result in a knee-like bending and a steepening above the knee. The topology of the individual knee positions shows a dependency on the primary particle. Though no hadronic interaction model is fully able to describe the multi-parameter data of KASCADE consistently, the more recent models or improved versions of older models reproduce the data better than few years ago.Comment: to appear in Nucl. Phys. B (Proc. Suppl.), Proc. of the XIII ISVHECRI, Pylos 2004 - with a better quality of the figure

Radio Emission in Atmospheric Air Showers: First Measurements with LOPES-30

When Ultra High Energy Cosmic Rays interact with particles in the Earth's atmosphere, they produce a shower of secondary particles propagating toward the ground. LOPES-30 is an absolutely calibrated array of 30 dipole antennas investigating the radio emission from these showers in detail and clarifying if the technique is useful for largescale applications. LOPES-30 is co-located and measures in coincidence with the air shower experiment KASCADE-Grande. Status of LOPES-30 and first measurements are presented.Comment: Proceedings of ARENA 06, June 2006, University of Northumbria, U

Dissecting the knee - Air shower measurements with KASCADE

Recent results of the KASCADE air shower experiment are presented in order to shed some light on the astrophysics of cosmic rays in the region of the knee in the energy spectrum. The results include investigations of high-energy interactions in the atmosphere, the analysis of the arrival directions of cosmic rays, the determination of the mean logarithmic mass, and the unfolding of energy spectra for elemental groups

The KASCADE-Grande Experiment and the LOPES Project

KASCADE-Grande is the extension of the multi-detector setup KASCADE to cover a primary cosmic ray energy range from 100 TeV to 1 EeV. The enlarged EAS experiment provides comprehensive observations of cosmic rays in the energy region around the knee. Grande is an array of 700 x 700 sqm equipped with 37 plastic scintillator stations sensitive to measure energy deposits and arrival times of air shower particles. LOPES is a small radio antenna array to operate in conjunction with KASCADE-Grande in order to calibrate the radio emission from cosmic ray air showers. Status and capabilities of the KASCADE-Grande experiment and the LOPES project are presented.Comment: To appear in Nuclear Physics B, Proceedings Supplements, as part of the volume for the CRIS 2004, Cosmic Ray International Seminar: GZK and Surrounding

Radio emission of highly inclined cosmic ray air showers measured with LOPES

LOPES-10 (the first phase of LOPES, consisting of 10 antennas) detected a significant number of cosmic ray air showers with a zenith angle larger than 50$^{\circ}$, and many of these have very high radio field strengths. The most inclined event that has been detected with LOPES-10 has a zenith angle of almost 80$^{\circ}$. This is proof that the new technique is also applicable for cosmic ray air showers with high inclinations, which in the case that they are initiated close to the ground, can be a signature of neutrino events.Our results indicate that arrays of simple radio antennas can be used for the detection of highly inclined air showers, which might be triggered by neutrinos. In addition, we found that the radio pulse height (normalized with the muon number) for highly inclined events increases with the geomagnetic angle, which confirms the geomagnetic origin of radio emission in cosmic ray air showers.Comment: A&A accepte

Radio detection of cosmic ray air showers with LOPES

In the last few years, radio detection of cosmic ray air showers has experienced a true renaissance, becoming manifest in a number of new experiments and simulation efforts. In particular, the LOPES project has successfully implemented modern interferometric methods to measure the radio emission from extensive air showers. LOPES has confirmed that the emission is coherent and of geomagnetic origin, as expected by the geosynchrotron mechanism, and has demonstrated that a large scale application of the radio technique has great potential to complement current measurements of ultra-high energy cosmic rays. We describe the current status, most recent results and open questions regarding radio detection of cosmic rays and give an overview of ongoing research and development for an application of the radio technique in the framework of the Pierre Auger Observatory.Comment: 8 pages; Proceedings of the CRIS2006 conference, Catania, Italy; to be published in Nuclear Physics B, Proceedings Supplement

Cosmic Ray Energy Spectra and Mass Composition at the Knee - Recent Results from KASCADE -

Recent results from the KASCADE experiment on measurements of cosmic rays in the energy range of the knee are presented. Emphasis is placed on energy spectra of individual mass groups as obtained from an two-dimensional unfolding applied to the reconstructed electron and truncated muon numbers of each individual EAS. The data show a knee-like structure in the energy spectra of light primaries (p, He, C) and an increasing dominance of heavy ones (A > 20) towards higher energies. This basic result is robust against uncertainties of the applied interaction models QGSJET and SIBYLL which are used in the shower simulations to analyse the data. Slight differences observed between experimental data and EAS simulations provide important clues for further improvements of the interaction models. The data are complemented by new limits on global anisotropies in the arrival directions of CRs and by upper limits on point sources. Astrophysical implications for discriminating models of maximum acceleration energy vs galactic diffusion/drift models of the knee are discussed based on this data.Comment: 8 pages, 7 figures, to appear in Nuclear Physics B, Proceedings Supplements, as part of the volume for the CRIS 2004, Cosmic Ray International Seminar: GZK and Surrounding