Intrinsically universal one-dimensional quantum cellular automata in two flavours

TL;DR

This paper introduces a one-dimensional quantum cellular automaton (QCA) that can simulate any other 1D QCA, with two variants requiring either infinite periodic or finite initial configurations, advancing the understanding of quantum computational universality.

Contribution

The paper presents the first intrinsic universal 1D QCA with two variants, one requiring infinite initial configurations and the other finite, enabling broad quantum simulation capabilities.

Findings

Universal QCA can simulate all 1D QCAs.

Simulation preserves topology with linear encoding.

Two flavors of universal QCA: weak and strong.

Abstract

We give a one-dimensional quantum cellular automaton (QCA) capable of simulating all others. By this we mean that the initial configuration and the local transition rule of any one-dimensional QCA can be encoded within the initial configuration of the universal QCA. Several steps of the universal QCA will 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. The encoding is linear and hence does not carry any of the cost of the computation. We do this in two flavours: a weak one which requires an infinite but periodic initial configuration and a strong one which needs only a finite initial configuration. KEYWORDS: Quantum cellular automata, Intrinsic universality, Quantum computation.