Towards practical classical processing for the surface code: timing analysis

Topological quantum error correction codes have high thresholds and are well suited to physical implementation. The minimum weight perfect matching algorithm can be used to efficiently handle errors in such codes. We perform a timing analysis of our current implementation of the minimum weight perfect matching algorithm. Our implementation performs the classical processing associated with an nxn lattice of qubits realizing a square surface code storing a single logical qubit of information in a fault-tolerant manner. We empirically demonstrate that our implementation requires only O(n^2) average time per round of error correction for code distances ranging from 4 to 512 and a range of depolarizing error rates. We also describe tests we have performed to verify that it always obtains a true minimum weight perfect matching.Comment: 13 pages, 13 figures, version accepted for publicatio

The Unveiling of Lodgism vs. Christianity: Positively Discussed Only In The Light of Its Most Friendly and Authorized Source of Information by Representative Men of God

https://digitalcommons.acu.edu/crs_books/1061/thumbnail.jp

Towards practical classical processing for the surface code

The surface code is unarguably the leading quantum error correction code for 2-D nearest neighbor architectures, featuring a high threshold error rate of approximately 1%, low overhead implementations of the entire Clifford group, and flexible, arbitrarily long-range logical gates. These highly desirable features come at the cost of significant classical processing complexity. We show how to perform the processing associated with an nxn lattice of qubits, each being manipulated in a realistic, fault-tolerant manner, in O(n^2) average time per round of error correction. We also describe how to parallelize the algorithm to achieve O(1) average processing per round, using only constant computing resources per unit area and local communication. Both of these complexities are optimal.Comment: 5 pages, 6 figures, published version with some additional tex

Magnetic Dipole Absorption of Radiation in Small Conducting Particles

We give a theoretical treatment of magnetic dipole absorption of electromagnetic radiation in small conducting particles, at photon energies which are large compared to the single particle level spacing, and small compared to the plasma frequency. We discuss both diffusive and ballistic electron dynamics for particles of arbitrary shape. The conductivity becomes non-local when the frequency is smaller than the frequency \omega_c characterising the transit of electrons from one side of the particle to the other, but in the diffusive case \omega_c plays no role in determining the absorption coefficient. In the ballistic case, the absorption coefficient is proportional to \omega^2 for \omega << \omega_c, but is a decreasing function of \omega for \omega >> \omega_c.Comment: 25 pages of plain TeX, 2 postscipt figure

The Role of the Radial Orbit Instability in Dark Matter Halo Formation and Structure

For a decade, N-body simulations have revealed a nearly universal dark matter density profile, which appears to be robust to changes in the overall density of the universe and the underlying power spectrum. Despite its universality, the physical origin of this profile has not yet been well understood. Semi--analytic models by Barnes et al. (2005) have suggested that the density structure of dark matter halos is determined by the onset of the radial orbit instability (ROI). We have tested this hypothesis using N-body simulations of collapsing dark matter halos with a variety of initial conditions. For dynamically cold initial conditions, the resulting halo structures are triaxial in shape, due to the mild aspect of the instability. We examine how variations in initial velocity dispersion affect the onset of the instability, and find that an isotropic velocity dispersion can suppress the ROI entirely, while a purely radial dispersion does not. The quantity sigma^2/vc^2 is a criterion for instability, where regions with sigma^2/vc^2 <~1 become triaxial due to the ROI or other perturbations. We also find that the radial orbit instability sets a scale length at which the velocity dispersion changes rapidly from isotropic to radially anisotropic. This scale length is proportional to the radius at which the density profile changes shape, as is the case in the semi--analytic models; however, the coefficient of proportionality is different by a factor of ~2.5. We conclude that the radial orbit instability is likely to be a key physical mechanism responsible for the nearly universal profiles of simulated dark matter halos.Comment: 13 pages, 12 figures, accepted to Ap

First record of Reticulitermes flavipes (Isoptera: Rhinotermitidae) from Terceira Island (Azores, Portugal)

Copyright © 2012 Florida Entomological Society.Reticulitermes flavipes, a Holarctic pestiferous subterranean termite species, particularly to structures and non-indigenous trees, is reported for the first time from Terceira Island, Azores, Portugal. The establishment of R. flavipes on Terceira Island likely represents more than one anthropogenic introduction with a high probability of military involvement