相关论文: A collective of stateless automata in a $n$-dimens…

To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…

We propose a discrete spacetime formulation of quantum electrodynamics in one-dimension (a.k.a the Schwinger model) in terms of quantum cellular automata, i.e. translationally invariant circuits of local quantum gates. These have exact…

Cellular Automata (CA), as they are presented in the literature, are abstract mathematical models of computation. In this pa- per we present an alternate approach: using the CA as a model or theory of physical systems and devices. While…

We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better…

We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…

The work is dedicated to the challenge: control and manipulation of the quantum state of a remote physical object. The goal is approached via the entanglement channel between the object and a local physical system - actuator - subjected to…

The sets of contexts and properties of a concept are embedded in the complex Hilbert space of quantum mechanics. States are unit vectors or density operators, and contexts and properties are orthogonal projections. The way calculations are…

The problem of finite/fixed-time cooperative state estimation is considered for a class of quasilinear systems with nonlinearities satisfying a H\"older condition. A strongly connected nonlinear distributed observer is designed under the…

Stators, which may be intuitively defined as "half states, half operators" are mathematical objects which act on two Hilbert spaces and utilize entanglement to create remote operations and exchange information between two physical systems.…

Complex environments, processes and systems may exhibit several distinct modes of physical behaviour or operation. Thus, for example, in their design, a set of mathematical models may be needed, each model having its own domain of…

We present a systematic simple method for constructing deterministic remote operations on single and multiple systems of arbitrary discrete dimensionality. These operations include remote rotations, remote interactions and measurements. The…

We consider the one-dimensional quantum mechanical problem of defining interactions concentrated at a single point in the framework of the theory of distributions. The often ill-defined product which describes the interaction term in the…

We show that when a quantum system is coupled to an environment in a mean field way, then its effective dynamics is governed by a unitary group with a time-dependent Hamiltonian. The time-dependent modification of the bare system…

We perform a numerical analysis of a recent introduced model for describing collective movement in alarmed animals groups. This model, derived from a position-based interaction and a limited attention field, displays a non-equilibrium phase…

Finite-state abstractions (a.k.a. symbolic models) present a promising avenue for the formal verification and synthesis of controllers in continuous-space control systems. These abstractions provide simplified models that capture the…

In the theory of point interactions, one is given a formal expression for a quantum mechanical Hamiltonian. The interaction terms of the Hamiltonian are singular: they can not be rigorously defined as a perturbation (in the operator or form…

The state complexity, respectively, nondeterministic state complexity of a regular language $L$ is the number of states of the minimal deterministic, respectively, of a minimal nondeterministic finite automaton for $L$. Some of the most…

A quantum mechanical model for the systems consisting of interacting bodies is considered. The model takes into account the noncommutativity of the space and impulse operators and the correlation equations for the indeterminacy of these…

In this paper, we reconsider the spin model suggested recently to understand some features of collective decision making among higher organisms [A.T. Hartnett et al., Phys. Rev. Lett. 116 (2016) 038701]. Within the model, the state of an…

Quantum robots and their interactions with environments of quantum systems are described and their study justified. A quantum robot is a mobile quantum system that includes a quantum computer and needed ancillary systems on board. Quantum…