Entanglement generation and self-correcting quantum memories

Building a working quantum computer that is able to perform useful calculations remains a challenge. With this thesis, we are trying to contribute a small piece to this puzzle by addressing three of the many fundamental questions one encounters along the way of reaching that goal. These questions are: (i) What is an easy way to create highly entangled states as a resource for quantum computation? (ii) What can we do to efficiently quantify states of noisy entanglement in systems coupled to the outside world? (iii) How can we protect and store fragile quantum states for arbitrary long times? The first two questions are the subject of part one of this thesis, `Entanglement Measures & Highly Entangled States'. We devise a particular proposal for generating entanglement within a solid-state setup, starting first with the tripartite case and continuing with a generalization to four and more qubits. The main idea there is to realize systems with highly entangled ground states in order for entanglement to be created by merely cooling to low enough temperatures. We have addressed the issue of quantifying entanglement in these systems by numerically calculating mixed-state entanglement measures and maximizing the latter as a function of the external magnetic field strength. The research along these lines has led to the development of the numerical library 'libCreme'. The second part of the thesis, 'Self-Correcting Quantum Memories', addresses the question how to reliably store quantum states long enough to perform useful calculations. Every computer, be it classical or quantum, needs the information it processes to be protected from corruption caused by faulty gates and perturbations from interactions with its environment. However, quantum states are much more susceptible to these adverse effects than classical states, making the manipulation and storage of quantum information a challenging task. Promising candidates for such 'quantum memories' are systems exhibiting topological order, because they are robust against local perturbations, and information encoded in their ground state can only be manipulated in a non-local fashion. We extend the so-called toric code by repulsive long-range interactions between anyons and show that this makes the code stable against thermal fluctuations. Furthermore, we investigate incoherent effects of quenched disorder in the toric code and similar systems

Quantum Computing with Electron Spins in Quantum Dots

Several topics on the implementation of spin qubits in quantum dots are reviewed. We first provide an introduction to the standard model of quantum computing and the basic criteria for its realization. Other alternative formulations such as measurement-based and adiabatic quantum computing are briefly discussed. We then focus on spin qubits in single and double GaAs electron quantum dots and review recent experimental achievements with respect to initialization, coherent manipulation and readout of the spin states. We extensively discuss the problem of decoherence in this system, with particular emphasis on its theoretical treatment and possible ways to overcome it.Comment: Lecture notes for Course CLXXI "Quantum Coherence in Solid State Systems" Int. School of Physics "Enrico Fermi", Varenna, July 2008, 61 pages, 20 figure

Highly Entangled Ground States in Tripartite Qubit Systems

We investigate the creation of highly entangled ground states in a system of three exchange-coupled qubits arranged in a ring geometry. Suitable magnetic field configurations yielding approximate GHZ and exact W ground states are identified. The entanglement in the system is studied at finite temperature in terms of the mixed-state tangle tau. By adapting a steepest-descent optimization algorithm we demonstrate that tau can be evaluated efficiently and with high precision. We identify the parameter regime for which the equilibrium entanglement of the tripartite system reaches its maximum.Comment: 4 pages, 2 figure

libCreme: An optimization library for evaluating convex-roof entanglement measures

We present the software library libCreme which we have previously used to successfully calculate convex-roof entanglement measures of mixed quantum states appearing in realistic physical systems. Evaluating the amount of entanglement in such states is in general a non-trivial task requiring to solve a highly non-linear complex optimization problem. The algorithms provided here are able to achieve to do this for a large and important class of entanglement measures. The library is mostly written in the Matlab programming language, but is fully compatible to the free and open-source Octave platform. Some inefficient subroutines are written in C/C++ for better performance. This manuscript discusses the most important theoretical concepts and workings of the algorithms, focussing on the actual implementation and usage within the library. Detailed examples in the end should make it easy for the user to apply libCreme to specific problems.Comment: 13 pages, 1 figure. The program code can be downloaded either from the CPC Library (http://cpc.cs.qub.ac.uk) or directly at http://quantumtheory.physik.unibas.ch/people/roethlisberger/libCreme.zi

New insights into the performance of human whole-exome capture platforms

Whole exome sequencing (WES) is increasingly used in research and diagnostics. WES users expect coverage of the entire coding region of known genes as well as sufficient read depth for the covered regions. It is, however, unknown which recent WES platform is most suitable to meet these expectations. We present insights into the performance of the most recent standard exome enrichment platforms from Agilent, NimbleGen and Illumina applied to six different DNA samples by two sequencing vendors per platform. Our results suggest that both Agilent and NimbleGen overall perform better than Illumina and that the high enrichment performance of Agilent is stable among samples and between vendors, whereas NimbleGen is only able to achieve vendor- and sample-specific best exome coverage. Moreover, the recent Agilent platform overall captures more coding exons with sufficient read depth than NimbleGen and Illumina. Due to considerable gaps in effective exome coverage, however, the three platforms cannot capture all known coding exons alone or in combination, requiring improvement. Our data emphasize the importance of evaluation of updated platform versions and suggest that enrichment-free whole genome sequencing can overcome the limitations of WES in sufficiently covering coding exons, especially GC-rich regions, and in characterizing structural variant

Incoherent dynamics in the toric code subject to disorder

We numerically study the effects of two forms of quenched disorder on the anyons of the toric code. Firstly, a new class of codes based on random lattices of stabilizer operators is presented, and shown to be superior to the standard square lattice toric code for certain forms of biased noise. It is further argued that these codes are close to optimal, in that they tightly reach the upper bound of error thresholds beyond which no correctable CSS codes can exist. Additionally, we study the classical motion of anyons in toric codes with randomly distributed onsite potentials. In the presence of repulsive long-range interaction between the anyons, a surprising increase with disorder strength of the lifetime of encoded states is reported and explained by an entirely incoherent mechanism. Finally, the coherent transport of the anyons in the presence of both forms of disorder is investigated, and a significant suppression of the anyon motion is found.Comment: 13 pages, 12 figure

Nachhaltigkeit in der Fremdfinanzierung : aktuelle Entwicklungen am Kapital- und Bankenmarkt und erwarteter Einfluss auf KMU

Nachhaltigkeitsüberlegungen haben sich im Anlagegeschäft zu einem festen Bestandteil von Investitionsstrategien entwickelt. Diese Entwicklungen werden zunehmend auch im Bereich der Unternehmensfinanzierung relevant. Davon betroffen sind aktuell vor allem Grossunternehmen, primär am Bond- und zunehmend auch am Kreditmarkt. KMU können von diesen Entwicklungen profitieren

[Reconstruction of a periodontally compromised dentition]

The presented case report describes a systematic treatment concept, the treatment sequence and the maintenance care of a sixty-seven-year old female patient suffering from generalized chronic periodontitis with advanced attachment loss. Due to a pretherapeutic risk assessment, several teeth were classified as "irrational to treat" or "doubtful". Therefore, a comprehensive reconstructive rehabilitation after active periodontal therapy was necessary. The restoration of a periodontally compromised dentition represents various difficulties. The patient wished to have fixed reconstructions. Depending upon anatomical conditions several different reconstructions were used: conventional bridges, partly using a resected molar root, a solely implant-retained bridge and a combined implant-tooth-retained bridge