Related papers: Maximum Independent Set via Probabilistic and Quan…
Cellular Automata are discrete-time dynamical systems on a spatially extended discrete space which provide paradigmatic examples of nonlinear phenomena. Their stochastic generalizations, i.e., Probabilistic Cellular Automata (PCA), are…
We study the Maximum Independent Set (MIS) problem on general graphs within the framework of learning-augmented algorithms. The MIS problem is known to be NP-hard and is also NP-hard to approximate to within a factor of $n^{1-\delta}$ for…
Quantum computing offers an alternative paradigm for addressing combinatorial optimization problems compared to classical computing. Despite recent hardware improvements, the execution of empirical quantum optimization experiments at scales…
Quantum finite automata can be used for pattern recognition. Present implementations on actual quantum devices face decoherence issues, which compromise the quality of long strings computation. In this work, we focus on the Measure Once…
There is nowhere else in emerging technology, but in Quantum-dot Cellular Automata, one can find high speed, low power operation, and high packaging density, which deals with electrostatic interaction between electrons within a cell.…
We present a hybrid adiabatic algorithm for maximum independent set (MIS) using Rydberg atom arrays. We engineer local controls that preferentially excite atoms with few neighbors, which represent graph nodes with small degrees. Numerical…
Most graphs in real life keep changing with time. These changes can be in the form of insertion or deletion of edges or vertices. Such rapidly changing graphs motivate us to study dynamic graph algorithms. However, three important graph…
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…
CA has grown as potential classifier for addressing major problems in bioinformatics. Lot of bioinformatics problems like predicting the protein coding region, finding the promoter region, predicting the structure of protein and many other…
One can think of some physical evolutions as being the emergent-effective result of a microscopic discrete model. Inspired by classical coarse-graining procedures, we provide a simple procedure to coarse-grain color-blind quantum cellular…
We propose a physical realization of quantum cellular automata (QCA) using arrays of ultracold atoms excited to Rydberg states. The key ingredient is the use of programmable multifrequency couplings which generalize the Rydberg blockade and…
Clifford quantum cellular automata (CQCAs) are a special kind of quantum cellular automata (QCAs) that incorporate Clifford group operations for the time evolution. Despite being classically simulable, they can be used as basic building…
Cellular Automata are discrete--time dynamical systems on a spatially extended discrete space which provide paradigmatic examples of nonlinear phenomena. Their stochastic generalizations, i.e., Probabilistic Cellular Automata, are discrete…
This article introduces new tools to study self-organisation in a family of simple cellular automata which contain some particle-like objects with good collision properties (coalescence) in their time evolution. We draw an initial…
We study PCA as a stochastic optimization problem and propose a novel stochastic approximation algorithm which we refer to as "Matrix Stochastic Gradient" (MSG), as well as a practical variant, Capped MSG. We study the method both…
Quantum cellular automata (QCAs) are automorphisms of tensor product algebras that preserve locality, with local quantum circuits as a simple example. We study approximate QCAs, where the locality condition is only satisfied up to a small…
Classical Cellular Automata (CCAs) are a powerful computational framework for modeling global spatio-temporal dynamics with local interactions. While CCAs have been applied across numerous scientific fields, identifying the local rule that…
Cellular automata are capable of developing complex behaviors based on simple local interactions between their elements. Some of these characteristics have been used to propose and improve meta-heuristics for global optimization; however,…
Simulations of one quantum system by an other has an implication in realization of quantum machine that can imitate any quantum system and solve problems that are not accessible to classical computers. One of the approach to engineer…
Starting from integrable cellular automata we present a novel form of Painlev\'e equations. These equations are discrete in both the independent variable and the dependent one. We show that they capture the essence of the behavior of the…