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Bibliographic Details
Main Authors: Wagner, Elisabeth, Dell'Anna, Federico, Nigmatullin, Ramil, Brennen, Gavin K.
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2404.05461
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author Wagner, Elisabeth
Dell'Anna, Federico
Nigmatullin, Ramil
Brennen, Gavin K.
author_facet Wagner, Elisabeth
Dell'Anna, Federico
Nigmatullin, Ramil
Brennen, Gavin K.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2404_05461
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Density Classification with Non-Unitary Quantum Cellular Automata
Wagner, Elisabeth
Dell'Anna, Federico
Nigmatullin, Ramil
Brennen, Gavin K.
Quantum Physics
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.
title Density Classification with Non-Unitary Quantum Cellular Automata
topic Quantum Physics
url https://arxiv.org/abs/2404.05461