Related papers: Unitarity in one dimensional nonlinear quantum cel…
For deterministic monotone cellular automata on the $d$-dimensional integer lattice, Toom has given necessary and sufficient conditions for the all-one fixed point to be stable against small random perturbations. The proof of sufficiency is…
We consider a class of quantum lattice models in $1+1$ dimensions represented as local quantum circuits that enjoy a particular "dual-unitarity" property. In essence, this property ensures that both the evolution "in time" and that "in…
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…
The model of cellular automata is fascinating because very simple local rules can generate complex global behaviors. The relationship between local and global function is subject of many studies. We tackle this question by using results on…
We introduce a scheme to perform universal quantum computation in quantum cellular automata (QCA) fashion in arbitrary subsystem dimension (not necessarily finite). The scheme is developed over a one spatial dimension $N$-element array,…
We derive a universal nonperturbative bound on the distance between unitary evolutions generated by time-dependent Hamiltonians in terms of the difference of their integral actions. We apply our result to provide explicit error bounds for…
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 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,…
The cellular automata with local permutation invariance are considered. We show that in the two-state case the set of such automata coincides with the generalized Game of Life family. We count the number of equivalence classes of the rules…
Linear acceleration theorems are known for most computational models. Although such results have been proved for two-dimensional cellular automata working on specific neighborhoods, no general construction was known. We present here a…
This paper examines whether unitary evolution alone is sufficient to explain emergence of the classical world from the perspective of computability theory. Specifically, it looks at the problem of how the choice related to the measurement…
In this paper the notion of quantum finite one-counter automata (QF1CA) is introduced. Introduction of the notion is similar to that of the 2-way quantum finite state automata by A.Kondacs and J.Watrous. The well-formedness conditions for…
Flexible Time is a new formalism for calculations about one-dimensional cellular automata. It unifies the states of a finite number of cells into a single object, even if they occur at different times. This gives greater flexibility to…
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…
The unitarity of quantum evolutions implies that the overlap between two initial states does not change in time. This property is commonly believed to explain the lack of state sensitivity in quantum theory, a feature that is prevailing in…
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…
We investigate the problem of what evolutions an open quantum system described by a time-local Master equation can undergo with universal coherent controls. A series of conditions are given which exclude channels from being reachable by any…
Particle-like objects are observed to propagate and interact in many spatially extended dynamical systems. For one of the simplest classes of such systems, one-dimensional cellular automata, we establish a rigorous upper bound on the number…
Dual-unitary circuits are a class of locally-interacting quantum many-body systems displaying unitary dynamics also when the roles of space and time are exchanged. These systems have recently emerged as a remarkable framework where certain…
The property of reversibility is quite meaningful for the classic theoretical computer science model, cellular automata. For the reversibility problem for a CA under null boundary conditions, while linear rules have been studied a lot, the…