Modern Approaches to Topological Quantum Error Correction

The construction of a large-scale fault-tolerant quantum computer is an outstanding scientific and technological goal. It holds the promise to allow us to solve a variety of complex problems such as factoring large numbers, quick database search, and the quantum simulation of many-body quantum systems in fields as diverse as condensed matter, quantum chemistry, and even high-energy physics. Sophisticated theoretical protocols for reliable quantum information processing under imperfect conditions have been de-veloped, when errors affect and corrupt the fragile quantum states during storage and computations. Arguably, the most realistic and promising ap-proach towards practical fault-tolerant quantum computation are topologi-cal quantum error-correcting codes, where quantum information is stored in interacting, topologically ordered 2D or 3D many-body quantum systems. This approach offers the highest known error thresholds, which are already today within reach of the experimental accuracy in state-of-the-art setups. A combination of theoretical and experimental research is needed to store, protect and process fragile quantum information in logical qubits effectively so that they can outperform their constituting physical qubits. Whereas small-scale quantum error correction codes have been implemented, one of the main theoretical challenges remains to develop new and improve existing efficient strategies (so-called decoders) to derive (near-)optimal error cor-rection operations in the presence of experimentally accessible measurement information and realistic noise sources. One main focus of this project is the development and numerical implementation of scalable, efficient decoders to operate topological color codes. Additionally, we study the feasibility of im-plementing quantum error-correcting codes fault-tolerantly in near-term ion traps. To this end, we use realistic modeling of the different noise sources, computer simulations, and most modern quantum information approaches to quantum circuitry and noise suppression techniques

The sounds of the Little and Big Bangs

Studies of heavy ion collisions have discovered that tiny fireballs of new phase of matter -- quark gluon plasma (QGP) -- undergoes explosion, called the Little Bang. In spite of its small size, it is not only well described by hydrodynamics, but even small perturbations on top of the explosion turned to be well described by hydrodynamical sound modes. The cosmological Big Bang also went through phase transitions, the QCD and electroweak ones, which are expected to produce sounds as well. We discuss their subsequent evolution and hypothetical inverse acoustic cascade, amplifying the amplitude. Ultimately, collision of two sound waves leads to formation of gravity waves, with the smallest wavelength. We briefly discuss how those can be detected.Comment: This paper is a short semi-popular review describing some recent developments in two very different fields, united by some common physics. It was written for the Universe journa

Nature of the Low Field Transition in the Mixed State of High Temperature Superconductors

We have numerically studied the statics and dynamics of a model three-dimensional vortex lattice at low magnetic fields. For the statics we use a frustrated 3D XY model on a stacked triangular lattice. We model the dynamics as a coupled network of overdamped resistively-shunted Josephson junctions with Langevin noise. At low fields, there is a weakly first-order phase transition, at which the vortex lattice melts into a line liquid. Phase coherence parallel to the field persists until a sharp crossover, conceivably a phase transition, near $T_{\ell} > T_m$ which develops at the same temperature as an infinite vortex tangle. The calculated flux flow resistivity in various geometries near $T=T_{\ell}$ closely resembles experiment. The local density of field induced vortices increases sharply near $T_\ell$, corresponding to the experimentally observed magnetization jump. We discuss the nature of a possible transition or crossover at $T_\ell$(B) which is distinct from flux lattice melting.Comment: Updated references. 46 pages including low quality 25 eps figures. Contact [email protected] or visit http://www.physics.ohio-state.edu:80/~ryu/ for better figures and additional movie files from simulations. To be published in Physical Review B1 01Jun9

Science Requirements and Conceptual Design for a Polarized Medium Energy Electron-Ion Collider at Jefferson Lab

This report presents a brief summary of the science opportunities and program of a polarized medium energy electron-ion collider at Jefferson Lab and a comprehensive description of the conceptual design of such a collider based on the CEBAF electron accelerator facility.Comment: 160 pages, ~93 figures This work was supported by the U.S. Department of Energy, Office of Nuclear Physics, under Contract No. DE-AC05-06OR23177, DE-AC02-06CH11357, DE-AC05-060R23177, and DESC0005823. The U.S. Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce this manuscript for U.S. Government purpose

Muon Spin Relaxation Study of MnGe and Development of Pair Distribution Function Methods

The first half of the thesis presents our experimental study of a helical magnet MnGe. We apply μSR technique to study the dynamic as well as the static magnetism in MnGe. Our key findings are as follows. From the muon dynamic relaxation 1/T1 results, no apparent critical behavior or anomaly was observed at the boundary between param- agnetic and the induced-ferromagnetic regions. Our study revealed linear relation between the transverse field relaxation rate and the static magnetization. Furthermore, their ratio, which can be regarded a form of hyperfine coupling constant, is very similar in the induced ferromagnetic region and the paramagnetic region. This suggest that the Z component of the Mn moment is static in both regions. On the other hand, the single relaxation rate in the transverse spectra suggest that the internal field is highly homogeneous in the induced ferromagnetic region. We therefore speculate that the induced ferromagnetic region and the paramagnetic region are not separate phases, but rather a single phase with different tendencies as temperature decrease. With decreasing temperature, the paramagnetic region is marked with the winning of the tendency towards ferromagnetic ordering over random ordering, and the induced ferromagnetic region is marked with the winning of the tendency towards the helical order over ferromagnetic order.At lower temperature, we observed dynamic critical behavior in the boundary between the induced ferromagnetic region and the Skyrmion region. Specifically, in low fields, the 1/T1 relaxation rate behaves qualitatively different from the prediction of SCR theory for itinerant ferromagnet for large temperature regime above Tc. In high fields, on the other hand, the system recovers the SCR itinerant ferromagnetic behavior. Through analyzing field effect on spin fluctuation and phase transition in the low and high field regimes, we speculate that this could be due to the suppression of helical fluctuation into ferromagnetic-like fluc- tuation by large magnetic fields. Our μSR results, which show 2nd order signature for the transition between the induced ferromagnetic region into the Skyrmion region, is consistent with considerations based on the topology of the magnetic structure in each phase. At low temperatures within the Skyrmion region of MnGe, our analysis of the transverse field data shows that all the three components of the Mn moment is frozen. The quadratic tempera- ture dependence of 1/T1 at low temperatures suggest the two-magnon spin wave to be the dominant spin excitation in the Skyrmion region. This is similar to those seen in local- ized moment magnets and is qualitatively different from the linear temperature dependence predicted from SCR theory for itinerant ferromagnets. The second half of the thesis present our derivation of the structure function and the pair distribution function (PDF) for textured materials. We also derive the analytical form of the PDF for a few special cases of texture. In this study, we start from the general form of a 3D structure function and derive the general and orientationally averaged form of the structure function and PDF for textured samples. In particular for a thin film sample with fibre texture, our formalism gives the result known as the 2 dimensional PDF. We developed open-software that calculates the 2 dimensional PDF for a textured thin film, and showed that the experimental PDF was well fitted using the model. On the other hand, the PDF method could be extended to an energy-dependent form, which could reveal explicitly the effect of lattice dynamics on the local arrangement of the atoms. This is usually called the dynamic PDF method. In this thesis we derive the analytical form of the dynamic PDF for a simple molecule that contains two identical atoms. And we interpret the mathematical results with physical consideration of the lattice dynamics. In addition, we also propose a new definition for the dynamic PDF which can be shown to reduce to the atomic PDF by integrating over energy. This new definition of the dynamic PDF incorporates the contribution from multi-phonon scattering effects, and can be computed conveniently from inelastic neutron scattering

Information Extraction and Modeling from Remote Sensing Images: Application to the Enhancement of Digital Elevation Models

To deal with high complexity data such as remote sensing images presenting metric resolution over large areas, an innovative, fast and robust image processing system is presented. The modeling of increasing level of information is used to extract, represent and link image features to semantic content. The potential of the proposed techniques is demonstrated with an application to enhance and regularize digital elevation models based on information collected from RS images