Threshold Error Penalty for Fault Tolerant Computation with Nearest Neighbour Communication

The error threshold for fault tolerant quantum computation with concatenated encoding of qubits is penalized by internal communication overhead. Many quantum computation proposals rely on nearest-neighbour communication, which requires excess gate operations. For a qubit stripe with a width of L+1 physical qubits implementing L levels of concatenation, we find that the error threshold of 2.1x10^-5 without any communication burden is reduced to 1.2x10^-7 when gate errors are the dominant source of error. This ~175X penalty in error threshold translates to an ~13X penalty in the amplitude and timing of gate operation control pulses.Comment: minor correctio

Sulfur reduction in sediments of marine and evaporite environments

Transformations of sulfur in sediments of ponds ranging in salinities from that of normal seawater to those of brines saturated with sodium chloride were examined. The chemistry of the sediment and pore waters were focused on with emphasis on the fate of sulfate reduction. The effects of increasing salinity on both forms of sulfur and microbial activity were determined. A unique set of chemical profiles and sulfate-reducing activity was found for the sediments of each of the sites examined. The quantity of organic matter in the salt pond sediments was significantly greater than that occurring in the adjacent intertidal site. The total quantitative and qualitative distribution of volatile fatty acids was also greater in the salt ponds. Volatile fatty acids increased with salinity

Exact Enumeration and Scaling for Fragmentation of Percolation Clusters

The fragmentation properties of percolation clusters yield information about their structure. Monte Carlo simulations and exact cluster enumeration for a square bond lattice and exact calculations for the Bethe lattice are used to study the fragmentation probability as(p) of clusters of mass s at an occupation probability p and the likelihood bs′s(p) that fragmentation of an s cluster will result in a daughter cluster of mass s′. Evidence is presented to support the scaling laws as(pc)∼s and bs′s(pc)=s-φg(s′/s), with φ=2-σ given by the standard cluster-number scaling exponent σ. Simulations for d=2 verify the finite-size-scaling form cs′sL(pc)=s1-φg̃(s′/s,s/Ldf) of the product cs′s(pc)=as(pc)bs′s(pc), where L is the lattice size and df is the fractal dimension. Exact calculations of the fragmentation probability fst of a cluster of mass s and perimeter t indicate that branches are important even on the maximum perimeter clusters. These calculations also show that the minimum of bs′s(p) near s′=s/2, where the two daughter masses are comparable, deepens with increasing p

Linear theory of unstable growth on rough surfaces

Unstable homoepitaxy on rough substrates is treated within a linear continuum theory. The time dependence of the surface width $W(t)$ is governed by three length scales: The characteristic scale $l_0$ of the substrate roughness, the terrace size $l_D$ and the Ehrlich-Schwoebel length $l_{ES}$. If $l_{ES} \ll l_D$ (weak step edge barriers) and $l_0 \ll l_m \sim l_D \sqrt{l_D/l_{ES}}$, then $W(t)$ displays a minimum at a coverage $\theta_{\rm min} \sim (l_D/l_{ES})^2$, where the initial surface width is reduced by a factor $l_0/l_m$. The r\^{o}le of deposition and diffusion noise is analyzed. The results are applied to recent experiments on the growth of InAs buffer layers [M.F. Gyure {\em et al.}, Phys. Rev. Lett. {\bf 81}, 4931 (1998)]. The overall features of the observed roughness evolution are captured by the linear theory, but the detailed time dependence shows distinct deviations which suggest a significant influence of nonlinearities

Beyond Blobs in Percolation Cluster Structure: The Distribution of 3-Blocks at the Percolation Threshold

The incipient infinite cluster appearing at the bond percolation threshold can be decomposed into singly-connected ``links'' and multiply-connected ``blobs.'' Here we decompose blobs into objects known in graph theory as 3-blocks. A 3-block is a graph that cannot be separated into disconnected subgraphs by cutting the graph at 2 or fewer vertices. Clusters, blobs, and 3-blocks are special cases of $k$-blocks with $k=1$, 2, and 3, respectively. We study bond percolation clusters at the percolation threshold on 2-dimensional square lattices and 3-dimensional cubic lattices and, using Monte-Carlo simulations, determine the distribution of the sizes of the 3-blocks into which the blobs are decomposed. We find that the 3-blocks have fractal dimension $d_3=1.2\pm 0.1$ in 2D and $1.15\pm 0.1$ in 3D. These fractal dimensions are significantly smaller than the fractal dimensions of the blobs, making possible more efficient calculation of percolation properties. Additionally, the closeness of the estimated values for $d_3$ in 2D and 3D is consistent with the possibility that $d_3$ is dimension independent. Generalizing the concept of the backbone, we introduce the concept of a ``$k$-bone'', which is the set of all points in a percolation system connected to $k$ disjoint terminal points (or sets of disjoint terminal points) by $k$ disjoint paths. We argue that the fractal dimension of a $k$-bone is equal to the fractal dimension of $k$-blocks, allowing us to discuss the relation between the fractal dimension of $k$-blocks and recent work on path crossing probabilities.Comment: All but first 2 figs. are low resolution and are best viewed when printe

A Hybrid Monte Carlo Method for Surface Growth Simulations

We introduce an algorithm for treating growth on surfaces which combines important features of continuum methods (such as the level-set method) and Kinetic Monte Carlo (KMC) simulations. We treat the motion of adatoms in continuum theory, but attach them to islands one atom at a time. The technique is borrowed from the Dielectric Breakdown Model. Our method allows us to give a realistic account of fluctuations in island shape, which is lacking in deterministic continuum treatments and which is an important physical effect. Our method should be most important for problems close to equilibrium where KMC becomes impractically slow.Comment: 4 pages, 5 figure