An algorithm for simulating the Ising model on a type-II quantum computer

Presented here is an algorithm for a type-II quantum computer which simulates the Ising model in one and two dimensions. It is equivalent to the Metropolis Monte-Carlo method and takes advantage of quantum superposition for random number generation. This algorithm does not require the ensemble of states to be measured at the end of each iteration, as is required for other type-II algorithms. Only the binary result is measured at each node which means this algorithm could be implemented using a range of different quantum computing architectures. The Ising model provides an example of how cellular automata rules can be formulated to be run on a type-II quantum computer.Comment: 14 pages, 11 figures. Accepted for publication in Computer Physics Communication

Topology regulates pattern formation capacity of binary cellular automata on graphs

We study the effect of topology variation on the dynamic behavior of a system with local update rules. We implement one-dimensional binary cellular automata on graphs with various topologies by formulating two sets of degree-dependent rules, each containing a single parameter. We observe that changes in graph topology induce transitions between different dynamic domains (Wolfram classes) without a formal change in the update rule. Along with topological variations, we study the pattern formation capacities of regular, random, small-world and scale-free graphs. Pattern formation capacity is quantified in terms of two entropy measures, which for standard cellular automata allow a qualitative distinction between the four Wolfram classes. A mean-field model explains the dynamic behavior of random graphs. Implications for our understanding of information transport through complex, network-based systems are discussed.Comment: 16 text pages, 13 figures. To be published in Physica

A guided tour of asynchronous cellular automata

Research on asynchronous cellular automata has received a great amount of attention these last years and has turned to a thriving field. We survey the recent research that has been carried out on this topic and present a wide state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat

Compression-based investigation of the dynamical properties of cellular automata and other systems

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 compression-based approach classifies cellular automata (CA) into clusters according to their heuristic behavior, with these clusters showing a correspondence with Wolfram's main classes of CA behavior. A compression based method to estimate a characteristic exponent to detect phase transitions and measure the resiliency or sensitivity of a system to its initial conditions is also proposed. A conjecture regarding the capability of a system to reach computational universality related to the values of this phase transition coefficient is formulated. These ideas constitute a compression-based framework for investigating the dynamical properties of cellular automata and other systems.Comment: 28 pages. This version includes the conjecture relating the transition coefficient to computational universality. Camera ready versio