Density Classification with Non-Unitary Quantum Cellular Automata
Abstract
The density classification (DC) task, a computation which maps global density information to local density, is studied using one-dimensional non-unitary quantum cellular automata (QCAs). Two approaches are considered: one that preserves the number density and one that performs majority voting. For number preserving DC, two QCAs are introduced that reach the fixed point solution in a time scaling quadratically with the system size. One of the QCAs is based on a known classical probabilistic cellular automaton which has been studied in the context of DC. The second is a new quantum model that is designed to demonstrate additional quantum features and is restricted to only two-body interactions. Both can be generated by continuous-time Lindblad dynamics. A third QCA is a hybrid rule defined by both discrete-time and continuous-time three-body interactions that is shown to solve the majority voting problem within a time that scales linearly with the system size.
Cite
@article{arxiv.2404.05461,
title = {Density Classification with Non-Unitary Quantum Cellular Automata},
author = {Elisabeth Wagner and Federico Dell'Anna and Ramil Nigmatullin and Gavin K. Brennen},
journal= {arXiv preprint arXiv:2404.05461},
year = {2025}
}
Comments
31 pages, 10 figures. (Update: Removed definitions from previous section I and minor corrections.)