Related papers: Unitary Quantum Cellular Automata for Density Clas…
Probabilistic cellular automata with deterministic updating are quantum systems. We employ the quantum formalism for an investigation of random probabilistic cellular automata, which start with a probability distribution over initial…
Quantum-dot Cellular Automata (QCA) as a nanoscale transistor-less device technology offers distinguishing advantages over the limitations of CMOS circuits. While more than 2 decades of design progress have been achieved with QCA, a…
We describe a class of cellular automata (CAs) that are end-to-end differentiable. DCAs interpolate the behavior of ordinary CAs through rules that act on distributions of states. The gradient of a DCA with respect to its parameters can be…
We study the fixed points of outer-totalistic cellular automata on sparse random regular graphs. These can be seen as constraint satisfaction problems, where each variable must adhere to the same local constraint, which depends solely on…
The expanding cellular automata (XCA) variant of cellular automata is investigated and characterized from a complexity-theoretical standpoint. An XCA is a one-dimensional cellular automaton which can dynamically create new cells between…
This paper studies three classes of cellular automata from a computational point of view: freezing cellular automata where the state of a cell can only decrease according to some order on states, cellular automata where each cell only makes…
Deterministic quantum computation with one quantum bit (DQC1) is a restricted model of quantum computing where the input state is the completely mixed state except for a single clean qubit, and only a single output qubit is measured at the…
In this dissertation, we study temporally stochasticity in cellular automata and the behavior of such cellular automata. The work also explores the computational ability of such cellular automaton that illustrates the computability of…
We present the algorithmic details of the dynamical cluster approximation (DCA) algorithm. The DCA is a fully-causal approach which systematically restores non-local correlations to the dynamical mean field approximation (DMFA). The DCA is…
Verifying uniform conditions over continuous spaces through random sampling is fundamental in machine learning and control theory, yet classical coverage analyses often yield conservative bounds, particularly at small failure probabilities.…
There have been several non-axiomatic approaches taken to define Quantum Cellular Automata (QCA). Partitioned QCA (PQCA) are the most canonical of these non-axiomatic definitions. In this work we first show that any QCA can be put into the…
We construct a novel three-dimensional quantum cellular automaton (QCA) based on a system with short-range entangled bulk and chiral semion boundary topological order. We argue that either the QCA is nontrivial, i.e. not a finite-depth…
Non-uniform cellular automata (NUCA) are an extension of cellular automata (CA), which transform cells according to multiple different local rules. A NUCA is defined by a configuration of local rules called a local rule distribution. We…
Quantum cellular automata (QCA) constitute space and time homogeneous discrete models for quantum field theories (QFTs). Although QFTs are defined without reference to particles, computations are done in terms of Feynman diagrams, which are…
We classify quantum cellular automata whose cells are qubits, on hypercubic lattices $\mathbb Z^s$, with the von Neumann neighborhood scheme, in terms of realizability as finite-depth quantum circuits. We show the most general structure of…
Neural cellular automata (NCA) provide a lightweight alternative to encoder-decoder segmentation networks. However, it can be difficult to decide when a prediction should be trusted. Here, we study uncertainty estimation for NCA-based…
Probing the ability of automata networks to solve decision problems has received a continuous attention in the literature, and specially with the automata reaching the answer by distributed consensus, i.e., their all taking on a same state,…
Recently, Land and Belew [Phys. Rev. Lett. 74, 5148 (1995)] have shown that no one-dimensional two-state cellular automaton which classifies binary strings according to their densities of 1's and 0's can be constructed. We show that a pair…
Layered Cellular Automata (LCA) extends the concept of traditional cellular automata (CA) to model complex systems and phenomena. In LCA, each cell's next state is determined by the interaction of two layers of computation, allowing for…
In this paper, we study reversibility of one-dimensional(1D) linear cellular automata(LCA) under null boundary condition, whose core problems have been divided into two main parts: calculating the period of reversibility and verifying the…