相关论文: Quantumness of discrete Hamiltonian cellular autom…

For non-uniform cellular automata (NUCA) with finite memory over an arbitrary universe with multiple local transition rules, we show that pointwise nilpotency, pointwise periodicity, and pointwise eventual periodicity properties are…

A digit function is presented which provides the $i$th-digit in base $p$ of any real number $x$. By means of this function, formulated within $\mathcal{B}$-calculus, the local, nonlocal and global dynamical behaviors of cellular automata…

We compare several definitions for number-conserving cellular automata that we prove to be equivalent. A necessary and sufficient condition for \cas to be number-conserving is proved. Using this condition, we give a linear-time algorithm to…

We build the coherent states for a family of solvable singular Schr\"odinger Hamiltonians obtained through supersymmetric quantum mechanics from the truncated oscillator. The main feature of such systems is the fact that their…

We introduce cellular automata whose cell spaces are left homogeneous spaces and prove a uniform as well as a topological variant of the Curtis-Hedlund-Lyndon theorem. Examples of left homogeneous spaces are spheres, Euclidean spaces, as…

We investigate dynamical many-body systems capable of universal computation, which leads to their properties being unpredictable unless the dynamics is simulated from the beginning to the end. Unpredictable behavior can be quantitatively…

We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits…

We illustrate an application of Algorithmic Information Dynamics to Cellular Automata (CA) demonstrating how this digital calculus is able to quantify change in discrete dynamical systems. We demonstrate the sensitivity of the Block…

In this paper we introduce the notion of quasi-expansivity for 2D CA and we show that it shares many properties with expansivity (that holds only for 1D CA). Similarly, we introduce the notions of quasi-sensitivity and prove that the…

It is well-known that time-dependent Schr\"{o}dinger equation can only be exactly solvable in very rare cases, even for two-level quantum systems. Therefore, finding exact quantum dynamics under time-dependent Hamiltonian is not only of…

We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm…

Recent advances on quantum foundations achieved the derivation of free quantum field theory from general principles, without referring to mechanical notions and relativistic invariance. From the aforementioned principles a quantum cellular…

Relation between global transition function and local transition function of a homogeneous one dimensional cellular automaton (CA) is investigated for some standard transition functions. It could be shown that left shift and right shift CA…

Currently there is great interest in computational models consisting of underlying regular computational environments, and built on them distributed computational structures. Examples of such models are cellular automata, spatial…

This thesis is split into two parts, which are united in the sense that they involve applying ideas from quantum information to fundamental physics. The first part is focused on examining discrete-time models in quantum computation…

A procedure allowing to construct rigorously discrete as well as continuum deterministic evolution equations from stochastic evolution equations is developed using a Dirac's bra and ket notation. This procedure is an extension of an…

Number-conserving cellular automata are discrete dynamical systems that simulate interacting particles like e.g. grains of sand. In an earlier paper, I had already derived a uniform construction for all transition rules of one-dimensional…

The commutators of the Poincar\'e group generators will be unchanged in form if a unitary transformation relates the free generators to the generators of an interacting relativistic theory. We test the concept of unitary transformations of…

Certain fermionic quantum field theories are equivalent to probabilistic cellular automata, with fermionic occupation numbers associated to bits. We construct an automaton that represents a discrete model of spinor gravity in four…

One-dimensional cellular automata are discrete dynamical systems that operate on an infinite lattice of sites and are characterized by the locality and uniformity of their update rule. Permutations of the state set and isometric…