Error tolerance of topological codes with independent bit-flip and measurement errors

Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be calculated by mapping the underlying quantum problem to a related classical statistical-mechanical spin system with quenched disorder. Here, we present results for the general fault-tolerant regime, where we consider both qubit and measurement errors. However, unlike in previous studies, here we vary the strength of the different error sources independently. Our results highlight peculiar differences between toric and color codes. This study complements previous results published in New J. Phys. 13, 083006 (2011).

A proposal for self-correcting stabilizer quantum memories in 3 dimensions (or slightly less)

We propose a family of local CSS stabilizer codes as possible candidates for self-correcting quantum memories in 3D. The construction is inspired by the classical Ising model on a Sierpinski carpet fractal, which acts as a classical self-correcting memory. Our models are naturally defined on fractal subsets of a 4D hypercubic lattice with Hausdorff dimension less than 3. Though this does not imply that these models can be realized with local interactions in R3, we also discuss this possibility. The X and Z sectors of the code are dual to one another, and we show that there exists a finite temperature phase transition associated with each of these sectors, providing evidence that the system may robustly store quantum information at finite temperature.

Lattice quantum codes and exotic topological phases of matter

This thesis addresses whether it is possible to build a robust memory device for quantum information. Many schemes for fault-tolerant quantum information processing have been developed so far, one of which, called topological quantum computation, makes use of degrees of freedom that are inherently insensitive to local errors. However, this scheme is not so reliable against thermal errors. Other fault-tolerant schemes achieve better reliability through active error correction, but incur a substantial overhead cost. Thus, it is of practical importance and theoretical interest to design and assess fault-tolerant schemes that work well at finite temperature without active error correction.

In this thesis, a three-dimensional gapped lattice spin model is found which demonstrates for the first time that a reliable quantum memory at finite temperature is possible, at least to some extent. When quantum information is encoded into a highly entangled ground state of this model and subjected to thermal errors, the errors remain easily correctable for a long time without any active intervention, because a macroscopic energy barrier keeps the errors well localized. As a result, stored quantum information can be retrieved faithfully for a memory time which grows exponentially with the square of the inverse temperature. In contrast, for previously known types of topological quantum storage in three or fewer spatial dimensions the memory time scales exponentially with the inverse temperature, rather than its square.

This spin model exhibits a previously unexpected topological quantum order, in which ground states are locally indistinguishable, pointlike excitations are immobile, and the immobility is not affected by small perturbations of the Hamiltonian. The degeneracy of the ground state, though also insensitive to perturbations, is a complicated number-theoretic function of the system size, and the system bifurcates into multiple noninteracting copies of itself under real-space renormalization group transformations. The degeneracy, the excitations, and the renormalization group flow can be analyzed using a framework that exploits the spin model's symmetry and some associated free resolutions of modules over polynomial algebras.

Constructing topological models by symmetrization: A projected entangled pair states study

Symmetrization of topologically ordered wave functions is a powerful method for constructing new topological models. Here we study wave functions obtained by symmetrizing quantum double models of a group G in the projected entangled pair states (PEPS) formalism. We show that symmetrization naturally gives rise to a larger symmetry group G˜ which is always non-Abelian. We prove that by symmetrizing on sufficiently large blocks, one can always construct wave functions in the same phase as the double model of G˜. In order to understand the effect of symmetrization on smaller patches, we carry out numerical studies for the toric code model, where we find strong evidence that symmetrizing on individual spins gives rise to a critical model which is at the phase transitions of two inequivalent toric codes, obtained by anyon condensation from the double model of G˜.

Topological SLAM Using Fast Vision Techniques

In this paper we propose a method for vision only topological simultaneous localisation and mapping (SLAM). Our approach does not use motion or odometric information but a sequence of colour histograms from visited places. In particular, we address the perceptual aliasing problem which occurs using external observations only in topological navigation. We propose a Bayesian inference method to incrementally build a topological map by inferring spatial relations from the sequence of observations while simultaneously estimating the robot's location. The algorithm aims to build a small map which is consistent with local adjacency information extracted from the sequence measurements. Local adjacency information is incorporated to disambiguate places which otherwise would appear to be the same. Experiments in an indoor environment show that the proposed technique is capable of dealing with perceptual aliasing using visual observations only and successfully performs topological SLAM.

Topological SLAM using neighbourhood information of places

Perceptual aliasing makes topological navigation a difficult task. In this paper we present a general approach for topological SLAM~(simultaneous localisation and mapping) which does not require motion or odometry information but only a sequence of noisy measurements from visited places. We propose a particle filtering technique for topological SLAM which relies on a method for disambiguating places which appear indistinguishable using neighbourhood information extracted from the sequence of observations. The algorithm aims to induce a small topological map which is consistent with the observations and simultaneously estimate the location of the robot. The proposed approach is evaluated using a data set of sonar measurements from an indoor environment which contains several similar places. It is demonstrated that our approach is capable of dealing with severe ambiguities and, and that it infers a small map in terms of vertices which is consistent with the sequence of observations.

A multi-hypothesis topological SLAM approach for loop closing on edge-ordered graphs

We present a method for topological SLAM that specifically targets loop closing for edge-ordered graphs. Instead of using a heuristic approach to accept or reject loop closing, we propose a probabilistically grounded multi-hypothesis technique that relies on the incremental construction of a map/state hypothesis tree. Loop closing is introduced automatically within the tree expansion, and likely hypotheses are chosen based on their posterior probability after a sequence of sensor measurements. Careful pruning of the hypothesis tree keeps the growing number of hypotheses under control and a recursive formulation reduces storage and computational costs. Experiments are used to validate the approach.

The utility and challenges of using ICD codes in child maltreatment research : a review of existing literature

Objective: The objectives of this article are to explore the extent to which the International Statistical Classification of Diseases and Related Health Problems (ICD) has been used in child abuse research, to describe how the ICD system has been applied and to assess factors affecting the reliability of ICD coded data in child abuse research.----- Methods: PubMed, CINAHL, PsychInfo and Google Scholar were searched for peer reviewed articles written since 1989 that used ICD as the classification system to identify cases and research child abuse using health databases. Snowballing strategies were also employed by searching the bibliographies of retrieved references to identify relevant associated articles. The papers identified through the search were independently screened by two authors for inclusion, resulting in 47 studies selected for the review. Due to heterogeneity of studies metaanalysis was not performed.----- Results: This paper highlights both utility and limitations of ICD coded data. ICD codes have been widely used to conduct research into child maltreatment in health data systems. The codes appear to be used primarily to determine child maltreatment patterns within identified diagnoses or to identify child maltreatment cases for research.----- Conclusions: A significant impediment to the use of ICD codes in child maltreatment research is the under-ascertainment of child maltreatment by using coded data alone. This is most clearly identified and, to some degree, quantified, in research where data linkage is used. Practice Implications: The importance of improved child maltreatment identification will assist in identifying risk factors and creating programs that can prevent and treat child maltreatment and assist in meeting reporting obligations under the CRC.

The Criminal Codes : Commentary and Materials

This edition has been substantially revised to increase overall clarity and to ensure a balanced examination of the criminal law in the 'Code' states, Queensland and Western Australia. The work has been brought up-to-date in all areas and provides valuable comment on the recent wide-reaching reforms to the law of homicide in Western Australia. Significant developments in both states discussed in this edition include: The abolition of wilful murder and infanticide, and the new definition of murder (WA); The introduction of the new offence of unlawful assault causing death (WA); The abolition of provocation to murder (WA), and whether this excuse still has a part to play (Qld); The reformulation of the excuse of self-defence, and the introduction of excessive self-defence (WA); The creation of offences for drink spiking (Qld and WA); and Current and proposed sentencing considerations (Qld and WA). Fundamental principles of the criminal law are illustrated throughout the book by selected extracts from the Codes and case law, while additional materials foster critical reflection on the law and the need for reform.

The effect of national governance codes on firm disclosure practices : evidence from analyst earnings forecasts

This study examines whether voluntary national governance codes have a significant effect on company disclosure practices. Two direct effects of the codes are expected: 1) an overall improvement in company disclosure practices, which is greater when the codes have a greater emphasis on disclosure; and 2) a leveling out of disclosure practices across companies (i.e., larger improvements in companies that were previously poorer disclosers) due to the codes new comply-or-explain requirements. The codes are also expected to have an indirect effect on disclosure practices through their effect on company governance practices. The results show that the introduction of the codes in eight East Asian countries has been associated with lower analyst forecast error and a leveling out of disclosure practices across companies. The codes are also found to have an indirect effect on company disclosure practices through their effect on board independence. This study shows that a regulatory approach to improving disclosure practices is not always necessary. Voluntary national governance codes are found to have both a significant direct effect and a significant indirect effect on company disclosure practices. In addition, the results indicate that analysts in Asia do react to changes in disclosure practices, so there is an incentive for small companies and family-owned companies to further improve their disclosure practices.

Vision-based topological mapping and localisation

Competent navigation in an environment is a major requirement for an autonomous mobile robot to accomplish its mission. Nowadays, many successful systems for navigating a mobile robot use an internal map which represents the environment in a detailed geometric manner. However, building, maintaining and using such environment maps for navigation is difficult because of perceptual aliasing and measurement noise. Moreover, geometric maps require the processing of huge amounts of data which is computationally expensive. This thesis addresses the problem of vision-based topological mapping and localisation for mobile robot navigation. Topological maps are concise and graphical representations of environments that are scalable and amenable to symbolic manipulation. Thus, they are well-suited for basic robot navigation applications, and also provide a representational basis for the procedural and semantic information needed for higher-level robotic tasks. In order to make vision-based topological navigation suitable for inexpensive mobile robots for the mass market we propose to characterise key places of the environment based on their visual appearance through colour histograms. The approach for representing places using visual appearance is based on the fact that colour histograms change slowly as the field of vision sweeps the scene when a robot moves through an environment. Hence, a place represents a region of the environment rather than a single position. We demonstrate in experiments using an indoor data set, that a topological map in which places are characterised using visual appearance augmented with metric clues provides sufficient information to perform continuous metric localisation which is robust to the kidnapped robot problem. Many topological mapping methods build a topological map by clustering visual observations to places. However, due to perceptual aliasing observations from different places may be mapped to the same place representative in the topological map. A main contribution of this thesis is a novel approach for dealing with the perceptual aliasing problem in topological mapping. We propose to incorporate neighbourhood relations for disambiguating places which otherwise are indistinguishable. We present a constraint based stochastic local search method which integrates the approach for place disambiguation in order to induce a topological map. Experiments show that the proposed method is capable of mapping environments with a high degree of perceptual aliasing, and that a small map is found quickly. Moreover, the method of using neighbourhood information for place disambiguation is integrated into a framework for topological off-line simultaneous localisation and mapping which does not require an initial categorisation of visual observations. Experiments on an indoor data set demonstrate the suitability of our method to reliably localise the robot while building a topological map.

Quality of cause-of-death reporting using ICD-10 drowning codes : a descriptive study of 69 countries

Background: The systematic collection of high-quality mortality data is a prerequisite in designing relevant drowning prevention programmes. This descriptive study aimed to assess the quality (i.e., level of specificity) of cause-of-death reporting using ICD-10 drowning codes across 69 countries.---------- Methods: World Health Organization (WHO) mortality data were extracted for analysis. The proportion of unintentional drowning deaths coded as unspecified at the 3-character level (ICD-10 code W74) and for which the place of occurrence was unspecified at the 4th character (.9) were calculated for each country as indicators of the quality of cause-of-death reporting.---------- Results: In 32 of the 69 countries studied, the percentage of cases of unintentional drowning coded as unspecified at the 3-character level exceeded 50%, and in 19 countries, this percentage exceeded 80%; in contrast, the percentage was lower than 10% in only 10 countries. In 21 of the 56 countries that report 4-character codes, the percentage of unintentional drowning deaths for which the place of occurrence was unspecified at the 4th character exceeded 50%, and in 15 countries, exceeded 90%; in only 14 countries was this percentage lower than 10%.---------- Conclusion: Despite the introduction of more specific subcategories for drowning in the ICD-10, many countries were found to be failing to report sufficiently specific codes in drowning mortality data submitted to the WHO.