Related papers: Quantum computation and real multiplication
The construction of anyonic operators and algebra is generalized by using quons operators. Therefore, the particular versionof fractional supersymmetry is constructed on the two-dimensional lattice by associating two generalized anyons of…
The Quantum Fourier Transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing Quantum Fourier Transform adders and multipliers and propose some modifications that extend their…
Using von Neumann algebras, we extend the theory of quantum computation on a graph to a theory of computation on an arbitrary topological space.
Quantum tori with graded involution appear as coordinate algebras of extended affine Lie algebras of type A_1, C and BC. We classify them in the category of algebras with involution. From this, we obtain precise information on the root…
Topological quantum computation may provide a robust approach for encoding and manipulating information utilizing the topological properties of anyonic quasi-particle excitations. We develop an efficient means to map between dense and…
The possibility of quantum computation using non-Abelian anyons has been considered for over a decade. However the question of how to obtain and process information about what errors have occurred in order to negate their effects has not…
Inspired by non-abelian vortex anyons in spinor Bose-Einstein condensates, we consider the quantum double $\mathcal{D}(Q_8)$ anyon model as a platform to carry out a particular instance of Shor's factorization algorithm. We provide the…
Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit of these exotic particles originated from…
We review the general strategy of topologically protected quantum information processing based on non-Abelian anyons, in which quantum information is encoded into the fusion channels of pairs of anyons and in fusion paths for multi-anyon…
Due to the existence of incompatible observables, the propositional calculus of a quantum system does not form a Boolean algebra but an orthomodular lattice. Such lattice can be realised as a lattice of subspaces on a real, complex or…
Topological quantum computation started as a niche area of research aimed at employing particles with exotic statistics, called anyons, for performing quantum computation. Soon it evolved to include a wide variety of disciplines. Advances…
Topological quantum computation employs two-dimensional quasiparticles called anyons. The generally accepted mathematical basis for the theory of anyons is the framework of modular tensor categories. That framework involves a substantial…
In this article we present a pedagogical introduction of the main ideas and recent advances in the area of topological quantum computation. We give an overview of the concept of anyons and their exotic statistics, present various models…
Anyons are quasiparticles in two-dimensional systems that show statistical properties very distinct from those of bosons or fermions. While their isolated observation has not yet been achieved, here we perform a quantum simulation of anyons…
Recent studies on quantum computing algorithms focus on excavating features of quantum computers which have potential for contributing to computational model enhancements. Among various approaches, quantum annealing methods effectively…
We present a quantum algorithm that additively approximates the value of a tensor network to a certain scale. When combined with existing results, this provides a complete problem for quantum computation. The result is a simple new way of…
We consider a two-dimensional spin system that exhibits abelian anyonic excitations. Manipulations of these excitations enable the construction of a quantum computational model. While the one-qubit gates are performed dynamically the model…
We present generalized and improved constructions for simulating quantum computers with a polynomial slowdown on lattices composed of qubits on which certain global versions of one- and two-qubit operations can be performed.
Quadratic algebras related to the reflection equations are introduced. They are quantum group comodule algebras. The quantum group $F_q(GL(2))$ is taken as the example. The properties of the algebras (center, representations, realizations,…
A great part of the mathematical foundations of topological quantum computation is given by the theory of modular categories which provides a description of the topological phases of matter such as anyon systems. In the near future the…