Related papers: Classification on the Computational Complexity of …
The concept of quantum complexity has far-reaching implications spanning theoretical computer science, quantum many-body physics, and high energy physics. The quantum complexity of a unitary transformation or quantum state is defined as the…
A major challenge of interdisciplinary description of complex system behaviour is whether real systems of higher complexity levels can be understood with at least the same degree of objective, "scientific" rigour and universality as…
We describe the Turing Machine, list some of its many influences on the theory of computation and complexity of computations, and illustrate its importance.
Simple constructions and protocols are demonstrated to allow the implementation of universal quantum computation on an arbitrarily large quantum system by controlling a fixed number of spins, vastly reducing the engineering requirements in…
We survey results on the topological complexity of classical configuration spaces of distinct ordered points in orientable surfaces and related spaces, including certain orbit configuration spaces and Eilenberg-Mac Lane spaces associated to…
We conjecture an algorithm to construct spin multipartitions and prove that all the level one Fock spaces using our combinatorics are modules over the quantum enveloping algebra.
Classical spin Hamiltonians are a powerful tool to model complex systems, characterised by a local structure given by the local Hamiltonians. One of the best understood local structures is the grammar of formal languages, which are central…
The classical soliton solution, quantized by means of suitable translational and rotational collective coordinates, is embedded into the one-particle irreductible representation of the Poincare group corresponding to a definite spin. It is…
We describe some field theoretic methods for studying quantum spin systems in one dimension. These include the nonlinear sigma-model approach which is particularly useful for large values of the spin, the idea of Luttinger liquids and…
Computational micromagnetics has become an indispensable tool for the theoretical investigation of magnetic structures. Classical micromagnetics has been successfully applied to a wide range of applications including magnetic storage media,…
This paper argues that the requirement of applicableness of quantum linearity to any physical level from molecules and atoms to the level of macroscopic extensional world, which leads to a main foundational problem in quantum theory…
Computational feasibility is a widespread concern that guides the framing and modeling of biological and artificial intelligence. The specification of cognitive system capacities is often shaped by unexamined intuitive assumptions about the…
The Hamiltonian cycle problem (HCP), which is an NP-complete problem, consists of having a graph G with n nodes and m edges and finding the path that connects each node exactly once. In this paper we compare some algorithms to solve a…
We present an alternative formalism for modeling spin. The ontological elements of this formalism are base-2 sequences of length $n$. The machinery necessary to model physics is then developed by considering correlations between base-2…
We examine classical and quantum aspects of the planar non-compact spin system coupled with Chern-Simons gauge field in the presence of background charge. We first define our classical spin system as non- relativistic non-linear sigma model…
This is the first of a series of papers in which we study deep computations (ultracomputations) and deep iterates, formalizing the ideas of "asymptotic limit" of computations and compositional iterates, respectively. In this first paper of…
The paper studies spin-orbit interaction (i.e. the effect the spin has on the particle's trajectory in a magnetic field) as a model of quantum computation. The two-level spin quantum system is examined using the stochastic mechanics…
A simple probabilistic cellular automaton is shown to be equivalent to a relativistic fermionic quantum field theory with interactions. Occupation numbers for fermions are classical bits or Ising spins. The automaton acts deterministically…
We discuss the problems of modeling, control, and decision support in complex dynamic systems from a general system theoretic point of view. The main characteristics of complex systems and of system approach to complex system study are…
We give a comprehensive review of the quantization of midisuperspace models. Though the main focus of the paper is on quantum aspects, we also provide an introduction to several classical points related to the definition of these models. We…