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Bijections between sets may be seen as discrete (or crisp) unitary transformations used in quantum computations. So discrete quantum cellular automata are cellular automata with reversible transition functions. This note studies on 1d…
Cellular automata are a discrete dynamical system which models massively parallel computation. Much attention is devoted to computations with small time complexity for which the parallelism may provide further possibilities. In this paper,…
The goal of this paper is to show why the framework of communication complexity seems suitable for the study of cellular automata. Researchers have tackled different algorithmic problems ranging from the complexity of predicting to the…
While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…
Quantum simulation, the simulation of quantum processes on quantum computers, suggests a path forward for the efficient simulation of problems in condensed-matter physics, quantum chemistry, and materials science. While the majority of…
We prove that endowing a real-time probabilistic or quantum computer with the ability of postselection increases its computational power. For this purpose, we provide a new model of finite automata with postselection, and compare it with…
We study a coarse-graining procedure for quantum cellular automata on hypercubic lattices that consists in grouping neighboring cells into tiles and selecting a subspace within each tile. This is done in such a way that multiple evolution…
We realize constant-space quantum computation by measure-many two-way quantum finite automata and evaluate their language recognition power by analyzing patterns of their exotic behaviors and by exploring their structural properties. In…
Effective quantum computation relies upon making good use of the exponential information capacity of a quantum machine. A large barrier to designing quantum algorithms for execution on real quantum machines is that, in general, it is…
We propose a discrete spacetime formulation of quantum electrodynamics in one-dimension (a.k.a the Schwinger model) in terms of quantum cellular automata, i.e. translationally invariant circuits of local quantum gates. These have exact…
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 show that any QCA can be put into the form…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Quantum…
A coarse-grained cellular automaton is proposed to simulate traffic systems. There, cells represent road sections. A cell can be in two states: jammed or passable. Numerical calculations are performed for a piece of square lattice with open…
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…
Cellular automata are a class of computational models based on simple rules and algorithms that can simulate a wide range of complex phenomena. However, when using conventional computers, these 'simple' rules are only encapsulated at the…
It is known that both quantum and classical cellular automata (CA) exist that are computationally universal in the sense that they can simulate, after appropriate initialization, any quantum or classical computation, respectively. Here we…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…
While there has been a keen interest in studying computation at the edge of chaos for dynamical systems undergoing a phase transition, this has come under question for cellular automata. We show that for continuously deformed cellular…
While quantum machine learning (ML) has been proposed to be one of the most promising applications of quantum computing, how to build quantum ML models that outperform classical ML remains a major open question. Here, we demonstrate a…