Related papers: Braided Categorical Quantum Mechanics I
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
This article develops a practical technique for studying representations of $\Bbbk$-linear categories arising in the categorification of quantum groups. We work in terms of locally unital algebras which are $\mathbb{Z}$-graded with graded…
After some historical remarks concerning Schroedinger's discovery of wave mechanics, we present a unified formalism for the mathematical description of classical and quantum-mechanical systems, utilizing elements of the theory of operator…
In this paper, I try once again to cause some good-natured trouble. The issue remains, when will we ever stop burdening the taxpayer with conferences devoted to the quantum foundations? The suspicion is expressed that no end will be in…
We study the categorical notion of braid gauging and obtain its classical Hopf algebraic description. We demonstrate how braid gauging can provide new insights on certain categorical invariants, such as the fusion rules and the higher…
A universal quantum computing scheme, with a universal set of logical gates, is proposed based on networks of 1D quantum systems. The encoding of information is in terms of universal features of gapped phases, for which effective field…
A data structure for finite bounded acyclic categories has been built, which is useful to encode and manipulate abstract orientable incidence structure. It can be represented as a directed acyclic multigraph with weighted edges, where the…
We present a number of quantum computing patterns that build on top of fundamental algorithms, that can be applied to solving concrete, NP-hard problems. In particular, we introduce the concept of a quantum dictionary as a summation of…
Recent developments in the theory of stability conditions and its relation to Teichmuller theory have revealed a deep connection between triangulated categories and surfaces. Motivated by this, we prove a categorical analogue of the…
Most ideas about what an algorithm is are very similar. Basic operations are used for transforming objects. The evaluation of internal and external states by relations has impact on the further process. A more precise definition can lead to…
Distributed quantum information processing seeks to overcome the scalability limitations of monolithic quantum devices by interconnecting multiple quantum processing nodes via classical and quantum communication. This approach extends the…
We apply the mechanism of factorization homology to construct and compute category-valued two-dimensional topological field theories associated to braided tensor categories, generalizing the $(0,1,2)$-dimensional part of…
The homotopy algebraic formalism of braided noncommutative field theory is used to define the explicit example of braided electrodynamics, that is, $\mathsf{U}(1)$ gauge theory minimally coupled to a Dirac fermion. We construct the braided…
We propose a taxonomy for quantum algorithms grounded in the fundamental symmetries, both continuous and discrete, underlying quantum state spaces, oracles, and circuit dynamics. By organizing algorithms according to their symmetry groups…
This paper defines the concept of an oriented quantum algebra and develops its application to the construction of quantum link invariants. We show that all known quantum link invariants can be put into this framework.
This paper introduces a category theory-based framework to redefine physical computing in light of advancements in quantum computing and non-standard computing systems. By integrating classical definitions within this broader perspective,…
We construct a category of flat vector bundles on an elliptic curve. It arises in the representation theory of quantum affine algebras and carries meromorphic braided structure with singularities on the diagonal of the square of the curve.
This dissertation has two main parts. The first part deals with questions relating to Haghverdi and Scott's notion of partially traced categories. The main result is a representation theorem for such categories: we prove that every…
This is a draft of the textbook/monograph that presents computability theory using string diagrams. The introductory chapters have been taught as graduate and undergraduate courses and evolved through 8 years of lecture notes. The later…
In Monoidal Computer I, we introduced a categorical model of computation where the formal reasoning about computability was supported by the simple and popular diagrammatic language of string diagrams. In the present paper, we refine and…