Partitioned quantum cellular automata are intrinsically universal

TL;DR

This paper demonstrates that all non-axiomatic definitions of Quantum Cellular Automata can be transformed into partitioned QCA, establishing their equivalence and intrinsic universality, which simplifies the model and advances theoretical understanding.

Contribution

It shows that any QCA can be expressed as a partitioned QCA, unifying different definitions and introducing a generalized intrinsic simulation framework.

Findings

All non-axiomatic QCA definitions are equivalent.

Any QCA can be simulated by a partitioned QCA.

The work introduces a generalized n-dimensional intrinsic simulation.

Abstract

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 of a PQCA. Our construction reconciles all the non-axiomatic definitions of QCA, showing that they can all simulate one another, and hence that they are all equivalent to the axiomatic definition. This is achieved by defining generalised n-dimensional intrinsic simulation, which brings the computer science based concepts of simulation and universality closer to theoretical physics. The result is not only an important simplification of the QCA model, it also plays a key role in the identification of a minimal n-dimensional intrinsically universal QCA.