Related papers: Non-abelian Quantum Statistics on Graphs

Quantum computation provides a unique opportunity to explore new regimes of physical systems through the creation of non-trivial quantum states far outside of the classical limit. However, such computation is remarkably sensitive to noise…

The theory of abelian categories proved very useful, providing an axiomatic framework for homology and cohomology of modules over a ring and, in particular, of abelian groups. For many years, a similar categorical framework has been lacking…

We study some topological aspects of non-abelian gauge theories intimately connected to the Lie algebras of the gauge groups and the homotopy theory in the generalized gauge orbit space. The physics connection to the non-perturbative…

An algorithm for quantum computing Hamiltonian cycles of simple, cubic, bipartite graphs is discussed. It is shown that it is possible to evolve a quantum computer into an entanglement of states which map onto the set of all possible paths…

We explain why, in a configuration space that is multiply connected, i.e., whose fundamental group is nontrivial, there are several quantum theories, corresponding to different choices of topological factors. We do this in the context of…

Non-Abelian topological orders offer an intriguing path towards fault-tolerant quantum computation, where information can be encoded and manipulated in a topologically protected manner immune to arbitrary local noises and perturbations.…

The fundamental notion of non-abelian generalized cohomology gained recognition in algebraic topology as the non-abelian Poincar\'e-dual to "factorization homology", and in theoretical physics as providing flux-quantization for non-linear…

In this paper, we will compute the non-abelian cohomology of the universal complete curve in positive characteristic. This extends Hain's result on the non-abelian cohomology of generic curves in characteristic zero to positive…

We study torsors over 2-groups and their morphisms. In particular, we study the first non-abelian cohomology group with values in a 2-group. Butterfly diagrams encode morphisms of 2-groups and we employ them to examine the functorial…

Quantum graphs have recently emerged as models of nonlinear optical, quantum confined systems with exquisite topological sensitivity and the potential for predicting structures with an intrinsic, off-resonance response approaching the…

Quantum walks are at the heart of modern quantum technologies. They allow to deal with quantum transport phenomena and are an advanced tool for constructing novel quantum algorithms. Quantum walks on graphs are fundamentally different from…

A new theoretical approach to non-equilibrium statistical systems has recently been proposed by the author, a co-author and others. It is based on a variational principle which is associated with the discrepancy of a path through…

This is an introduction to work on the generalisation to quantum groups of Mackey's approach to quantisation on homogeneous spaces. We recall the bicrossproduct models of the author, which generalise the quantum double. We describe the…

We derive an intuitive and novel method to represent nodes in a graph with special unitary operators, or quantum operators, which does not require parameter training and is competitive with classical methods on scoring similarity between…

Mapping complex input data into suitable lower dimensional manifolds is a common procedure in machine learning. This step is beneficial mainly for two reasons: (1) it reduces the data dimensionality and (2) it provides a new data…

We uncover the very rich graph topology of generic bounded non-Hermitian spectra, distinct from the topology of conventional band invariants and complex spectral winding. The graph configuration of complex spectra are characterized by the…

A universal quantum computer can be constructed using abelian anyons. Two qubit quantum logic gates such as controlled-NOT operations are performed using topological effects. Single-anyon operations such as hopping from site to site on a…

We study quantization of a class of inhomogeneous Lie bialgebras which are crossproducts in dual sectors with Abelian invariant parts. This class forms a category stable under dualization and the double operations. The quantization turns…

Higher gauge theory for non-abelian structure 2-groups faces significant challenges when extending beyond the fake-flat sector, which suffers from limited applicability in physical models. A promising resolution involves equipping 2-groups…

In spite of their evident logical character, particle statistics symmetries are not among the inherently quantum features exploited in quantum computation. A difficulty may be that, being a constant of motion of a unitary evolution, a…