Related papers: Density Classification with Non-Unitary Quantum Ce…
Elementary cellular automata (ECA) present iconic examples of complex systems. Though described only by one-dimensional strings of binary cells evolving according to nearest-neighbour update rules, certain ECA rules manifest complex…
We provide algebraic criteria for the unitarity of linear quantum cellular automata, i.e. one dimensional quantum cellular automata. We derive these both by direct combinatorial arguments, and by adding constraints into the model which do…
This study presents a unitary quantum cellular automaton (QCA) that, in the continuum limit, converges to the (1+1)-dimensional Generalized Dirac Equation (GDE). We outline the construction of the unitary, discrete-time evolution and derive…
Quantum-dot cellular automata (QCA) is a low-power, non-von-Neumann, general-purpose paradigm for classical computing using transistor-free logic. An elementary QCA device called a "cell" is made from a system of coupled quantum dots with a…
We study probabilistic cellular automata (PCA) and quantum cellular automata (QCA) as frameworks for solving the Maximum Independent Set (MIS) problem. We first introduce a synchronous PCA whose dynamics drives the system toward the…
It has been shown that uniform as well as non-uniform cellular automata (CA) can be evolved to perform certain computational tasks. Random Boolean networks are a generalization of two-state cellular automata, where the interconnection…
Quantum algorithms are touted as a way around some classically intractable problems such as the simulation of quantum mechanics. At the end of all quantum algorithms is a quantum measurement whereby classical data is extracted and utilized.…
This paper presents a strategy for efficient quantum circuit design for density estimation. The strategy is based on a quantum-inspired algorithm for density estimation and a circuit optimisation routine based on memetic algorithms. The…
We present a method for computing probability of occurence of 1s in a configuration obtained by iteration of a probabilistic cellular automata (PCA), starting from a random initial configuration. If the PCA is sufficiently simple, one can…
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…
A method for studying the qualitative dynamical properties of abstract computing machines based on the approximation of their program-size complexity using a general lossless compression algorithm is presented. It is shown that the…
A one-dimensional two-state number-conserving cellular automaton (NCCA) is a cellular automaton whose states are 0 or 1 and where cells take states 0 and 1 and updated their states by the rule which keeps overall sum of states constant. It…
Cellular automata (CA) exemplify systems where simple local interaction rules can lead to intricate and complex emergent phenomena at large scales. The various types of dynamical behavior of CA are usually categorized empirically into…
A new kind of cellular automaton (CA) for the study of the dynamics of urban systems is proposed. The state of a cell is not described using a finite set, but by means of continuum variables. A population sector is included, taking into…
We investigate the possibility to have electron-pairs in dephasing-free subspace (DFS), by means of the quantum-dot cellular automata (QCA) and single-spin rotations, to carry out a high-fidelity and deterministic universal quantum…
Understanding the quantum control landscape (QCL) is important for designing effective quantum control strategies. In this study, we analyze the QCL for a single two-level quantum system (qubit) using various control strategies. We employ…
Quantum computing is concerned with computer technology based on the principles of quantum mechanics, with operations performed at the quantum level. Quantum computational models make it possible to analyze the resources required for…
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…
Quantum density matrix represents all the information of the entire quantum system, and novel models of meaning employing density matrices naturally model linguistic phenomena such as hyponymy and linguistic ambiguity, among others in…
This work introduces a new problem, named as, affinity classification problem which is a generalization of the density classification problem. To solve this problem, we introduce temporally stochastic cellular automata where two rules are…