Topological phases of matter, Quantum Error Correction and Topological twist

Unitary Modular Tensor Categories(UMTC) have a one-to-one correspondence with Topological Quantum Field Theories (TQFT). Different identifications have been made so far associating different physical particle types (anyons) to different UMTCs. However, the area of anyon model transformations has not been discovered much, which correspond to topological phase transitions. Physical condensation of particles (quasi-particles) can correspond to functors between different UMTCs. This paper discusses a special case of doubled semion condensation. We also give an error detection and correction algorithm for the Doubled Semion model which is more efficient than the previously suggested ones. At last, we present some results about twisting the underlying lattice structure and see its effects on UMTCs and logical subspaces e.g., for Ising, Doubled Semion models, and a combination of these. This suggests some interesting "wormholes" phenomenon.Comment: 21 pages, 22 figure

The Bonahon-Wong-Yang volume conjecture for the four-puncture sphere

We compute the Bonahon-Wong-Yang quantum invariant for self-diffeomorphisms of the four-puncture sphere explicitly, based on the representation theory of the Checkov-Fock algebra. As an application of the computation, we verify the volume conjecture proposed by Bonahon-Wong-Yang for the four puncture sphere bundles with some technical conditions. Together with the one-puncture torus bundles, this is the first family of examples for which the conjecture is verified providing evidence for the conjectur

Topological Characterization with a Twist, Condensation, and Reflection

Despite its putative robustness, the realization of and control over topological quantum matter is an ongoing grand challenge. Looking forward, robust characterization protocols are needed to first certify topological substrates before they are utilized in quantum algorithms. We contribute to this grand challenge by providing a series of experimentally accessible near- and medium-term protocols assessing the fidelity of logical processes. To do so we examine logical operators and anyonic quasiparticle excitations in twisted $\mathbb{Z}_{N=2,4}$ gauge theories. Extending the finite twist, a promising route to Ising computing in its own right, to a non-contractible twist fuses prior logical operators together and results in a twisted qubit code. The code is notable for a doubled and tripled code distance for logical $Y$ and $X$ errors respectively. Next, we review the deconfinement properties of a $\mathbb{Z}_4$ double semion condensation and provide an error correction algorithm. Based on this understanding we then present a $\mathbb{Z}_4$ topological quasiparticle reflectometry and scattering protocol. The protocol infers the topological properties of the system and serves as a high-level metric for the performance and lifetime of the interfaced topological codes. Our logical and scattering protocols are suitable for near-term devices where many physical qubits encode few logical qubits. The topological lifetime of a particle within a condensate conjugacy class, previously considered in fabricated and hetero-structured condensed-matter experiments, serves as a unifying performance metric across synthetic, qubit-based, and naturally occurring topological order.Comment: 6 pages, 4 figure

An Environmentally Stable and Lead-Free Chalcogenide Perovskite

Organic-inorganic halide perovskites are intrinsically unstable when exposed to moisture and/or light. Additionally, the presence of lead in many perovskites raises toxicity concerns. Herein is reported a thin film of BaZrS3, a lead-free chalcogenide perovskite. Photoluminescence and X-ray diffraction measurements show that BaZrS3 is far more stable than methylammonium lead iodide (MAPbI3) in moist environments. Moisture- and light-induced degradations in BaZrS3 and MAPbI3 are compared by using simulations and calculations based on density functional theory. The simulations reveal drastically slower degradation in BaZrS3 due to two factors - weak interaction with water, and very low rates of ion migration. BaZrS3 photo-detecting devices with photo-responsivity of ~46.5 mA W-1 are also reported. The devices retain ~60% of their initial photo-response after 4 weeks in ambient conditions. Similar MAPbI3 devices degrade rapidly and show ~95% decrease in photo-responsivity in just 4 days. The findings establish the superior stability of BaZrS3 and strengthen the case for its use in optoelectronics. New possibilities for thermoelectric energy conversion using these materials are also demonstrated

Geometry of fundamental shadow link complements and applications to the 1-loop conjecture

We construct a geometric ideal triangulation for every fundamental shadow link complement and solve the gluing equation explicitly in terms of the holonomies of the meridians of the link for any generic character in the distinguished component of the $\mathrm{PSL}(2;\mathbb{C})$-character variety of the link complement. As an application, we obtain a new formula for the volume of a hyperideal tetrahedron in terms of its dihedral angles. Moreover, by using the ideal triangulation, we verify the 1-loop conjecture proposed by Dimofte and Garoufalidis for every fundamental shadow link complement. We also prove a surgery formula for the 1-loop invariant with respect to certain nice ideal triangulations of 3-manifolds with toroidal boundary.Comment: 52 pages, 22 figure

Generalized Bonahon-Wong-Yang volume conjecture of quantum invariants of surface diffeomorphisms I: the figure eight knot complement

We propose a generalization of the Bonahon-Wong-Yang volume conjecture of quantum invariants of surface diffeomorphisms, by relating the asymptotics of the invariants with certain hyperbolic cone structure on the mapping torus determined by the choice of the invariant puncture weights. We prove the conjecture for the once-punctured torus bundle with the diffeomorphism given by the word $LR$.Comment: 29 pages, 1 figur

Assessing State of the Art on Artificial Neural Network Paradigms for Level of Eutrophication Estimation of Water Bodies

With growing power of computer and blend of intelligent soft wares, the interpretation and analytical capabilities of the system had shown an excellent growth, providing intelligence solutions to almost every computing problem. In this direction here we are trying to identify how different geocomputation techniques had been implemented for estimation of parameters on water bodies so as to identify the level of contamination leading to the different level of eutrophication. The main mission of this paper is to identify state-of-art in artificial neural network paradigms that are prevailing and effective in modeling and combining spatial data for anticipation. Among this, our interest is to identify different analysis techniques and their parameters that are mainly used for quality inspection of lakes and estimation of nutrient pollutant content in it, and different neural network models that offered the forecasting of level of eutrophication in the water bodies. Different techniques are analyzed over the main steps;-assimilation of spatial data, statistical interpretation technique, observed parameters used for eutrophication estimation and accuracy of resultant data

Electronic Word-of-Mouth: Impact on Music Sales in the American Market

Internet, today, is a popular communication and feedback sharing platform. Digital content is also readily available over the internet. These two phenomena have propelled the electronic interaction among music consumers to new heights. Our study investigates the contribution of electronic word-of-mouth (eWOM) to the sales of music albums. We studied the American music market for 13 consecutive weeks. The Sales data for these weeks was correlated to the eWOM data for the period mentioned before