A Simple n-Dimensional Intrinsically Universal Quantum Cellular Automaton

TL;DR

This paper introduces a simple n-dimensional quantum cellular automaton that can simulate any other QCA, encoding their initial configurations and evolution within its own structure, thus serving as an intrinsically universal model.

Contribution

It presents a new, simple n-dimensional quantum cellular automaton that is capable of universal simulation of all other QCAs, preserving topology and encoding their dynamics.

Findings

The universal QCA can simulate any n-dimensional QCA.

Simulation preserves the topology of the original QCA.

Multiple steps of the universal QCA correspond to one step of the simulated QCA.

Abstract

We describe a simple n-dimensional quantum cellular automaton (QCA) capable of simulating all others, in that the initial configuration and the forward evolution of any n-dimensional QCA can be encoded within the initial configuration of the intrinsically universal QCA. Several steps of the intrinsically universal QCA then correspond to one step of the simulated QCA. The simulation preserves the topology in the sense that each cell of the simulated QCA is encoded as a group of adjacent cells in the universal QCA.