Related papers: Quantum Fibrations: quantum computation on an arbi…
This thesis is concerned with the application of operadic methods, particularly modular operads, to questions arising in the study of moduli spaces of surfaces as well as applications to the study of homotopy algebras and new constructions…
We aim to explore if inside a quantum vertex algebras, we can find the right notion of a quantum conformal algebra.
We review "quantum" invariants of closed oriented 3-dimensional manifolds arising from operator algebras.
Starting from a recently-introduced algebraic structure on spin foam models, we define a Hopf algebra by dividing with an appropriate quotient. The structure, thus defined, naturally allows for a mirror analysis of spin foam models with…
Two-dimensional topological states of matter offer a route to quantum computation that would be topologically protected against the nemesis of the quantum circuit model: decoherence. Research groups in industry, government and academic…
In mathematical aspect, we introduce quantum algorithm and the mathematical structure of quantum computer. Quantum algorithm is expressed by linear algebra on a finite dimensional complex inner product space. The mathematical formulations…
The tomographic description of a quantum state is formulated in an abstract infinite dimensional Hilbert space framework, the space of the Hilbert-Schmidt linear operators, with trace formula as scalar product. Resolutions of the unity,…
Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local Hamiltonian H for a time t. In contrast to this quantum engineering,…
We study the construction of both universal quantum computation and multi-partite entangled states in the topological diagrammatical approach to quantum teleportation. Our results show that the teleportation-based quantum circuit model…
We construct canonical quantum fields which propagate on a star graph modeling a quantum wire. The construction uses a deformation of the algebra of canonical commutation relations, encoding the interaction in the vertex of the graph. We…
We propose a definition of quantum computable functions as mappings between superpositions of natural numbers to probability distributions of natural numbers. Each function is obtained as a limit of an infinite computation of a quantum…
This work has the purpose of applying the concept of Geometric Calculus (Clifford Algebras) to the Fibre Bundle description of Quantum Mechanics. Thus, it is intended to generalize that formulation to curved spacetimes [the base space of…
Quantum computing (QC) is a new computational paradigm whose foundations relate to quantum physics. Notable progress has been made, driving the birth of a series of quantum-based algorithms that take advantage of quantum computational…
The method of Feynman-Kac perturbation of quantum stochastic processes has a long pedigree, with the theory usually developed within the framework of processes on von Neumann algebras. In this work, the theory of operator spaces is…
: Algebraic properties of orbifold models on arbitrary Riemann surfaces are investigated. The action of mapping class group transformations and of standard geometric operations is given explicitly. An infinite dimensional extension of the…
Quantum Field Theory (QFT) represents a vast generalization of Quantum Mechanics (QM), as it deals with systems that have an infinite number of degrees of freedom. The Stone-von Neumann theorem, which establishes the equivalence of…
We study the relation between quantum computational complexity and general relativity. The quantum computational complexity is proposed to be quantified by the shortest length of geodesic quantum curves. We examine the complexity/volume…
We consider the quantum processor based on a chain of trapped ions to propose an architecture wherein the motional degrees of freedom of trapped ions (position and momentum) could be exploited as the computational Hilbert space. We adopt a…
A finite discrete graph is turned into a quantum (metric) graph once a finite length is assigned to each edge and the one-dimensional Laplacian is taken to be the operator. We study the dependence of the spectral gap (the first positive…
Quantum supermaps are higher-order maps transforming quantum operations into quantum operations. Here we extend the theory of quantum supermaps, originally formulated in the finite dimensional setting, to the case of higher-order maps…