## Fricke Topological Qubits

We recently proposed that topological quantum computing might be based on SL(2,C) representations of the fundamental group π1(S3\K) for the complement of a link K in the three-sphere. The restriction to links whose associated SL(2,C) character variety V contains a Fricke surface κd=xyz−x2−y2−z2+d is desirable due to the connection of Fricke spaces to elementary topology. Taking K as the Hopf link L2a1, one of the three arithmetic two-bridge links (the […]

## DNA Sequence and Structure under the Prism of Group Theory and Algebraic Surfaces

Taking a DNA sequence, a word with letters/bases A, T, G and C, as the relation between the generators of an infinite group π, one can discriminate between two important families: (i) the cardinality structure for conjugacy classes of subgroups of π is that of a free group on one to four bases, and the […]

## Exploiting Anyonic Behavior of Quasicrystals for Topological Quantum Computing

The concrete realization of topological quantum computing using low-dimensional quasiparticles, known as anyons, remains one of the important challenges of quantum computing. A topological quantum computing platform promises to deliver more robust qubits with additional hardware-level protection against errors that could lead to the desired large-scale quantum computation. We propose quasicrystal materials as such a […]

## Character Varieties and Algebraic Surfaces for the Topology of Quantum Computing

It is shown that the representation theory of some finitely presented groups thanks to their $SL_2(\mathbb{C})$ character variety is related to algebraic surfaces. We make use of the Enriques-Kodaira classification of algebraic surfaces and the related topological tools to make such surfaces explicit. We study the connection of $SL_2(\mathbb{C})$ character varieties to topological quantum computing […]

## Synthesis of the Ti-Zr-Ni alloys by the “hydride cycle” method

A comprehensive study of the technical parameters and conditions for the synthesis of ternary alloys in the Ti-Zr-Ni system by the “hydride cycle” method was carried out. The influence on the synthesis process of such parameters as: temperature and annealing time, heating rate, cooling conditions, material composition, dispersion, hydrogen content in the hydrides used, the […]