Fault-tolerant quantum computation with cluster states

The one-way quantum computing model introduced by Raussendorf and Briegel [Phys. Rev. Lett. 86, 5188 (2001)] shows that it is possible to quantum compute using only a fixed entangled resource known as a cluster state, and adaptive single-qubit measurements. This model is the basis for several practical proposals for quantum computation, including a promising proposal for optical quantum computation based on cluster states [M. A. Nielsen, Phys. Rev. Lett. (to be published), quant-ph/0402005]. A significant open question is whether such proposals are scalable in the presence of physically realistic noise. In this paper we prove two threshold theorems which show that scalable fault-tolerant quantum computation may be achieved in implementations based on cluster states, provided the noise in the implementations is below some constant threshold value. Our first threshold theorem applies to a class of implementations in which entangling gates are applied deterministically, but with a small amount of noise. We expect this threshold to be applicable in a wide variety of physical systems. Our second threshold theorem is specifically adapted to proposals such as the optical cluster-state proposal, in which nondeterministic entangling gates are used. A critical technical component of our proofs is two powerful theorems which relate the properties of noisy unitary operations restricted to act on a subspace of state space to extensions of those operations acting on the entire state space. We expect these theorems to have a variety of applications in other areas of quantum-information science.

A 2D numerical model for simulating the physics of fault systems

Simulations provide a powerful means to help gain the understanding of crustal fault system physics required to progress towards the goal of earthquake forecasting. Cellular Automata are efficient enough to probe system dynamics but their simplifications render interpretations questionable. In contrast, sophisticated elasto-dynamic models yield more convincing results but are too computationally demanding to explore phase space. To help bridge this gap, we develop a simple 2D elastodynamic model of parallel fault systems. The model is discretised onto a triangular lattice and faults are specified as split nodes along horizontal rows in the lattice. A simple numerical approach is presented for calculating the forces at medium and split nodes such that general nonlinear frictional constitutive relations can be modeled along faults. Single and multi-fault simulation examples are presented using a nonlinear frictional relation that is slip and slip-rate dependent in order to illustrate the model.

Apparent strain localization and shear wave dispersion in elastic fault gouge with microrotations

Shear deformation of fault gouge or other particulate materials often results in observed strain localization, or more precisely, the localization of measured deformation gradients. In conventional elastic materials the strain localization cannot take place therefore this phenomenon is attributed to special types of non-elastic constitutive behaviour. For particulate materials however the Cosserat continuum which takes care of microrotations independent of displacements is a more appropriate model. In elastic Cosserat continuum the localization in displacement gradients is possible under some combinations of the generalized Cosserat elastic moduli. The same combinations of parameters also correspond to a considerable dispersion in shear wave propagation which can be used for independent experimental verification of the proposed mechanism of apparent strain localization in fault gouge.

Convective instability of 3-D fluid-saturated geological fault zones heated from below

We conduct a theoretical analysis to investigate the convective instability of 3-D fluid-saturated geological fault zones when they are heated uniformly from below. In particular, we have derived exact analytical solutions for the critical Rayleigh numbers of different convective flow structures. Using these critical Rayleigh numbers, three interesting convective flow structures have been identified in a geological fault zone system. It has been recognized that the critical Rayleigh numbers of the system have a minimum value only for the fault zone of infinite length, in which the corresponding convective flow structure is a 2-D slender-circle flow. However, if the length of the fault zone is finite, the convective flow in the system must be 3-D. Even if the length of the fault zone is infinite, since the minimum critical Rayleigh number for the 2-D slender-circle flow structure is so close to that for the 3-D convective flow structure, the system may have almost the same chance to pick up the 3-D convective flow structures. Also, because the convection modes are so close for the 3-D convective flow structures, the convective flow may evolve into the 3-D finger-like structures, especially for the case of the fault thickness to height ratio approaching zero. This understanding demonstrates the beautiful aspects of the present analytical solution for the convective instability of 3-D geological fault zones, because the present analytical solution is valid for any value of the ratio of the fault height to thickness. Using the present analytical solution, the conditions, under which different convective flow structures may take place, can be easily determined.

Double diffusion-driven convective instability of three-dimensional fluid-saturated geological fault zones heated from below

We conduct a theoretical analysis to investigate the double diffusion-driven convective instability of three-dimensional fluid-saturated geological fault zones when they are heated uniformly from below. The fault zone is assumed to be more permeable than its surrounding rocks. In particular, we have derived exact analytical solutions to the total critical Rayleigh numbers of the double diffusion-driven convective flow. Using the corresponding total critical Rayleigh numbers, the double diffusion-driven convective instability of a fluid-saturated three-dimensional geological fault zone system has been investigated. The related theoretical analysis demonstrates that: (1) The relative higher concentration of the chemical species at the top of the three-dimensional geological fault zone system can destabilize the convective flow of the system, while the relative lower concentration of the chemical species at the top of the three-dimensional geological fault zone system can stabilize the convective flow of the system. (2) The double diffusion-driven convective flow modes of the three-dimensional geological fault zone system are very close each other and therefore, the system may have the similar chance to pick up different double diffusion-driven convective flow modes, especially in the case of the fault thickness to height ratio approaching 0. (3) The significant influence of the chemical species diffusion on the convective instability of the three-dimensional geological fault zone system implies that the seawater intrusion into the surface of the Earth is a potential mechanism to trigger the convective flow in the shallow three-dimensional geological fault zone system.

Numerical simulation of double-diffusion driven convective flow and rock alteration in three-dimensional fluid-saturated geological fault zones

Numerical methods are used to simulate the double-diffusion driven convective pore-fluid flow and rock alteration in three-dimensional fluid-saturated geological fault zones. The double diffusion is caused by a combination of both the positive upward temperature gradient and the positive downward salinity concentration gradient within a three-dimensional fluid-saturated geological fault zone, which is assumed to be more permeable than its surrounding rocks. In order to ensure the physical meaningfulness of the obtained numerical solutions, the numerical method used in this study is validated by a benchmark problem, for which the analytical solution to the critical Rayleigh number of the system is available. The theoretical value of the critical Rayleigh number of a three-dimensional fluid-saturated geological fault zone system can be used to judge whether or not the double-diffusion driven convective pore-fluid flow can take place within the system. After the possibility of triggering the double-diffusion driven convective pore-fluid flow is theoretically validated for the numerical model of a three-dimensional fluid-saturated geological fault zone system, the corresponding numerical solutions for the convective flow and temperature are directly coupled with a geochemical system. Through the numerical simulation of the coupled system between the convective fluid flow, heat transfer, mass transport and chemical reactions, we have investigated the effect of the double-diffusion driven convective pore-fluid flow on the rock alteration, which is the direct consequence of mineral redistribution due to its dissolution, transportation and precipitation, within the three-dimensional fluid-saturated geological fault zone system. (c) 2005 Elsevier B.V. All rights reserved.

Prevalence of Metabolic Syndrome in Patients With Intermittent Claudication and its Correlation With the Segment of Arterial Obstruction

The metabolic syndrome (MetS) is associated with increased cardiovascular morbidity and mortality. Intermittent claudication reflects the presence of peripheral arterial disease (PAD). The aim of this study is to determine the prevalence of the MetS in claudicants and its correlation with age, gender, localization of arterial obstruction, and symptomatic coronary disease. Patients (n = 170) with intermittent claudication were studied. The mean age was 65 years (33-89). Metabolic syndrome was diagnosed in 98 patients (57.6%). The mean age of patients with MetS was 63.5 years compared with 67.0 years for patients without MetS (P = .027). Considering patients aged >= 65 years, MetS was present in 46 (48.9%) individuals and in 52 (68.4%) patients younger than 65 years (P = .011). Metabolic syndrome must be actively searched for in claudicant patients.

Partial lesions of the intratemporal segment of the facial nerve: Graft versus partial reconstruction

Objectives: In cases of partial lesions of the intratemporal segment of the facial nerve, should the surgeon perform an intraoperative partial reconstruction, or partially remove the injured segment and place a graft? We present results from partial lesion reconstruction on the intratemporal segment of the facial nerve. Methods: A retrospective study on 42 patients who presented partial lesions on the intratemporal segment of the facial nerve was performed between 1988 and 2005. The patients were divided into 3 groups based on the procedure used: interposition of the partial graft on the injured area of the nerve (group 1; 12 patients); keeping the preserved part and performing tubulization (group 2; 8 patients); and dividing the parts of the injured nerve (proximal and distal) and placing a total graft of the sural nerve (group 3; 22 patients). Results: Fracture of the temporal bone was the most frequent cause of the lesion in all groups, followed by iatrogenic causes (p < 0.005). Those who obtained results lower than or equal to III on the House-Brackmann scale were 1 (8.3%) of the patients in group 1, none (0.0%) of the patients in group 2, and 15 (68.2%) of the patients in group 3 (p < 0.001). Conclusions: The best surgical technique for therapy of a partial lesion of the facial nerve is still questionable. Among these 42 patients, the best results were those from the total graft of the facial nerve.

Skin Coverage of the Middle-Distal Segment of the Leg With a Pedicled Perforator Flap

Objective: This is a clinical study of our experience using pedicle perforator flaps to cover skin defects in the middle and distal segment of the leg. Design: Prospective study. Setting: University hospital. Patients/Intervention: Twenty-four patients underwent treatment of a skin defect in the middle or distal segment of the leg by means of pedicled flaps based on perforating arteries. The perforating arteries were located before the operation by means of echo-Doppler examination. The flaps were planned in propeller fashion (21 cases) and as advancement (three cases). Main Outcome Measurements: The results were evaluated according the origin of perforator flap, size of the flap, and donor area and viability of the flap. The success rate of the echo-Doppler to identify the location of perforator vessel was also evaluated. Results: In nine cases, the perforating vessels originated from the fibular artery, in 10 the posterior tibial artery, and in five the anterior tibial artery. The mean size of the flaps was 5 cm in width by 12 cm in length. The success rate using an echo-Doppler was 87%. The flaps were fully viable in 20 cases and partially viable in four cases. Conclusion: On the basis of these results, it is concluded that perforating flaps are a good choice of treatment for skin losses, especially in the distal segment of the leg, and could be an alternative option for the use of free microsurgical flaps.

Lower uterine segment thickness measurement in pregnant women with previous Cesarean section: reliability analysis using two- and three-dimensional transabdominal and transvaginal ultrasound

Objective To evaluate the reliability of two- and three-dimensional ultrasonographic measurement of the thickness of the lower uterine segment (LUS) in pregnant women by transvaginal and transabdominal approaches. Methods This was a study of 30 pregnant women who bad bad at least one previous Cesarean section and were between 36 and 39 weeks` gestation, with singleton pregnancies in cephalic presentation. Sonographic examinations were performed by two observers using both 4-7-MHz transabdominal and 5-8-MHz transvaginal volumetric probes. LUS measurements were performed using two- and three-dimensional ultrasound, evaluating the entire LUS thickness transabdominally and the LUS muscular thickness transvaginally. Each observer measured the LUS four times by each method. Reliability was analyzed by comparing the mean of the absolute differences, the intraclass correlation coefficients, the 95% limits of agreement and the proportion of differences <1 mm. Results Transvaginal ultrasound provided greater reliability in LUS measurements than did transabdominal ultrasound. The use of three-dimensional ultrasound improved significantly the reliability of the LUS muscular thickness measurement obtained transvaginally. Conclusions Ultrasonographic measurement of the LUS muscular thickness transvaginally appears more reliable than does that of the entire LUS thickness transabdominally. The use of three-dimensional ultrasound should be considered to improve measurement reliability. Copyright (c) 2009 ISUOG. Published by John Wiley & Sons, Ltd.

A sensitive vorticity gauge using rotated porphyroblasts, and its application to rocks adjacent to the Alpine Fault, New Zealand

Variable aspect ratio porphyroblasts deformed in non-coaxial flow. and internally containing rotated relicts of an external foliation, can be used to characterise plane strain flow regimes. The distribution obtained by plotting the orientation of the long axis of such grains, classified by aspect ratio, against the orientation of the internal foliation is potentially a sensitive gauge of both the bulk shear strain (as previously suggested) and kinematic vorticity number. We illustrate the method using rotated biotite porphyroblasts in the Alpine Schist: a sequence of mid-crustal rocks that have been ramped to the surface along the Alpine Fault. a major transpressional plate boundary. Results indicate that, at distances greater than or equal to similar to1 km from the fault, the rocks have undergone a combination of irrotational fattening and dextral-oblique, normal-sense shear, with a bulk shear strain of similar to0.6 and kinematic vorticity number of similar to0.2. The vorticity analysis is compatible with estimates of strongly oblate bulk strain of similar to 75% maximum shortening. Dextral-reverse transpressional flow characterises higher strain S-tectonite mylonite within similar to1 km of the Alpine Fault. These relationships provide insight into the kinematics of flow and distribution of strain in the hangingwall of the Alpine Fault and place constraints on numerical mechanical models for the exhumation of these mid-crustal rocks. (C) 2001 Elsevier Science Ltd. All rights reserved.