A Quantum Game of Life
Pablo Arrighi, Jonathan Grattage
TL;DR
This paper introduces a minimal, universal three-dimensional quantum cellular automaton (QCA) within the partitioned QCA subclass, capable of simulating all other 3D QCA with elegant signal and gate structures.
Contribution
It presents the first minimal universal 3D PQCA with block size 2x2x2 and cell dimension 2, demonstrating a simple yet powerful quantum automaton model.
Findings
Constructed a minimal universal 3D PQCA
Signals, wires, and gates emerge naturally in the model
Capable of simulating all other 3D QCA
Abstract
This research describes a three dimensional quantum cellular automaton (QCA) which can simulate all other 3D QCA. This intrinsically universal QCA belongs to the simplest subclass of QCA: Partitioned QCA (PQCA). PQCA are QCA of a particular form, where incoming information is scattered by a fixed unitary U before being redistributed and rescattered. Our construction is minimal amongst PQCA, having block size 2 x 2 x 2 and cell dimension 2. Signals, wires and gates emerge in an elegant fashion.
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