On one-dimensional quantum cellular automata

2002 ◽  
Author(s):  
J. Watrous
Keyword(s):  
Cellular Automata ◽  
Quantum Cellular Automata ◽  
One Dimensional

scholarly journals Remarks on the Structure of Clifford Quantum Cellular Automata

2009 ◽  
Vol 16 (02n03) ◽  
pp. 269-279
Author(s):  
Dirk-Michael Schlingemann
Keyword(s):  
Phase Space ◽  
Cellular Automata ◽  
Symplectic Group ◽  
Tensor Products ◽  
Projective Representation ◽  
Dimensional Case ◽  
Additional Restriction ◽  
Quantum Cellular Automata ◽  
One Dimensional ◽  
The One

We report here on the structure of reversible quantum cellular automata with the additional restriction that these are also Clifford operations. This means that tensor products of Weyl operators (projective representation of a finite abelian symplectic group) are mapped to multiples of tensor products of Weyl operators. Therefore Clifford quantum cellular automata are induced by symplectic cellular automata in phase space. We characterize these symplectic cellular automata and find that all possible local rules must be, up to some global shift, reflection-invariant with respect to the origin. In the one-dimensional case we also find that all 1D Clifford quantum cellular automata are generated by a few elementary operations.

Intrinsically Universal One-dimensional Quantum Cellular Automata in Two Flavours

2009 ◽  
Vol 91 (2) ◽  
pp. 197-230
Author(s):  
Pablo Arrighi ◽  
Renan Fargetton ◽  
Zizhu Wang
Keyword(s):  
Cellular Automata ◽  
Quantum Cellular Automata ◽  
One Dimensional

Novel quantum image encryption using one-dimensional quantum cellular automata

2016 ◽  
Vol 345 ◽  
pp. 257-270 ◽  
Author(s):  
Yu-Guang Yang ◽  
Ju Tian ◽  
He Lei ◽  
Yi-Hua Zhou ◽  
Wei-Min Shi
Keyword(s):  
Cellular Automata ◽  
Image Encryption ◽  
Quantum Cellular Automata ◽  
Quantum Image ◽  
One Dimensional ◽  
Quantum Image Encryption

scholarly journals Reversibility and quantum coherence in one-dimensional quantum cellular automata

2018 ◽  
Vol 98 (1) ◽  
Author(s):  
Federico Centrone ◽  
Camillo Tassi ◽  
Marco Barbieri ◽  
Alessio Serafini
Keyword(s):  
Cellular Automata ◽  
Quantum Coherence ◽  
Quantum Cellular Automata ◽  
One Dimensional
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