Density Classification with Non-Unitary Quantum Cellular Automata
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 n...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/27/1/26 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832588595717734400 |
|---|---|
| author | Elisabeth Wagner Federico Dell’Anna Ramil Nigmatullin Gavin K. Brennen |
| author_facet | Elisabeth Wagner Federico Dell’Anna Ramil Nigmatullin Gavin K. Brennen |
| author_sort | Elisabeth Wagner |
| collection | DOAJ |
| description | 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 | Article |
| id | doaj-art-fbdd7c7a13894db9b1a385fd9c77cf5c |
| institution | Kabale University |
| issn | 1099-4300 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-fbdd7c7a13894db9b1a385fd9c77cf5c2025-01-24T13:31:43ZengMDPI AGEntropy1099-43002024-12-012712610.3390/e27010026Density Classification with Non-Unitary Quantum Cellular AutomataElisabeth Wagner0Federico Dell’Anna1Ramil Nigmatullin2Gavin K. Brennen3School of Mathematical and Physical Sciences, Macquarie University, Sydney, NSW 2109, AustraliaDipartimento di Fisica e Astronomia, Università di Bologna, I-40127 Bologna, ItalySchool of Mathematical and Physical Sciences, Macquarie University, Sydney, NSW 2109, AustraliaSchool of Mathematical and Physical Sciences, Macquarie University, Sydney, NSW 2109, AustraliaThe 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.https://www.mdpi.com/1099-4300/27/1/26quantum cellular automatadensity classificationmajority problemquantum computingquantum simulationopen quantum systems |
| spellingShingle | Elisabeth Wagner Federico Dell’Anna Ramil Nigmatullin Gavin K. Brennen Density Classification with Non-Unitary Quantum Cellular Automata Entropy quantum cellular automata density classification majority problem quantum computing quantum simulation open quantum systems |
| title | Density Classification with Non-Unitary Quantum Cellular Automata |
| title_full | Density Classification with Non-Unitary Quantum Cellular Automata |
| title_fullStr | Density Classification with Non-Unitary Quantum Cellular Automata |
| title_full_unstemmed | Density Classification with Non-Unitary Quantum Cellular Automata |
| title_short | Density Classification with Non-Unitary Quantum Cellular Automata |
| title_sort | density classification with non unitary quantum cellular automata |
| topic | quantum cellular automata density classification majority problem quantum computing quantum simulation open quantum systems |
| url | https://www.mdpi.com/1099-4300/27/1/26 |
| work_keys_str_mv | AT elisabethwagner densityclassificationwithnonunitaryquantumcellularautomata AT federicodellanna densityclassificationwithnonunitaryquantumcellularautomata AT ramilnigmatullin densityclassificationwithnonunitaryquantumcellularautomata AT gavinkbrennen densityclassificationwithnonunitaryquantumcellularautomata |