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Reversible quantum cellular automata [article]

B. Schumacher, R.F. Werner
2004 arXiv   pre-print
We present several construction methods for quantum cellular automata, based on unitaries commuting with their translates, on the quantization of (arbitrary) reversible classical cellular automata, on  ...  This implies that, in contrast to the classical case, the inverse of a nearest neighbor quantum cellular automaton is again a nearest neighbor automaton.  ...  The structural invertibility was an open problem in the theory of classical reversible cellular automata in higher dimensional lattices until recently [15] .  ... 
arXiv:quant-ph/0405174v1 fatcat:df3dx2zuezd65glrd7saosk2vy

Cellular Automata: Reversibility, Semi-reversibility and Randomness [article]

Kamalika Bhattacharjee
2019 arXiv   pre-print
In this dissertation, we study two of the global properties of 1-dimensional cellular automata (CAs) under periodic boundary condition, namely, reversibility and randomness.  ...  To address reversibility of finite CAs, we develop a mathematical tool, named reachability tree, which can efficiently characterize those CAs.  ...  There are many interesting results regarding reversibility of 1-dimensional CAs, over a given local map R, for the first three cases: Theorem 4.1 : The following statements hold for 1-dimensional infinite  ... 
arXiv:1911.03609v1 fatcat:522xu4usonfdbguuckurl4eeqi

On the reversibility and the closed image property of linear cellular automata

Tullio Ceccherini-Silberstein, Michel Coornaert
2011 Theoretical Computer Science  
When G is an arbitrary group and V is a finite-dimensional vector space, it is known that every bijective linear cellular automaton τ V^G → V^G is reversible and that the image of every linear cellular  ...  We also show that if G is a non-periodic group and V is an infinite-dimensional vector space, then there exist a linear cellular automaton τ_1 V^G → V^G which is bijective but not reversible and a linear  ...  Although classical symbolic dynamics often restricts to the case when the alphabet set A is finite, it is clear from recent developments in the theory, such as the ones contained in the influential work  ... 
doi:10.1016/j.tcs.2010.09.020 fatcat:2wct3xu6xfbr7mgpgmq3qm4hou

Reversibility in one-dimensional quantum cellular automata in the presence of noise [article]

Federico Centrone, Camillo Tassi, Alessio Serafini, Marco Barbieri
2018 arXiv   pre-print
We consider a class of noisy, one-dimensional quantum cellular automata that allow one to shift from unitary dynamics to completely positive maps, and investigate the notion of reversibility in such a  ...  To this aim, we associate an approximate reverse automaton to each noisy automaton, and assess its effect, and we define an irreversibility time based on the distance from the maximally mixed state, which  ...  Reversible cellular automata form a natural model of reversible computing.  ... 
arXiv:1801.02060v1 fatcat:efrx257v6rdmxkohhqqn47d2ja

Efficient Synthesis of Reversible Circuits Using Quantum Dot Cellular Automata

Ahmed Moustafa, Ahmed Younes
2021 IEEE Access  
A quantum-dot cellular automaton (QCA) is nano-electronics technology which can be used to build reversible circuits [2] [3] .  ...  Reversible logic gates [12] , or reversible transformations, are operations applied on a register to perform the computation by changing the states of the system from one state to another.  ... 
doi:10.1109/access.2021.3083507 fatcat:jhnc4qznj5bxlngexydhovbvcm

Quantum Cellular Automata [article]

K. Wiesner
2008 arXiv   pre-print
Quantum cellular automata (QCA) are reviewed, including early and more recent proposals. QCA are a generalization of (classical) cellular automata (CA) and in particular of reversible CA.  ...  An overview is given over early attempts by various authors to define one-dimensional QCA. These turned out to have serious shortcomings which are discussed as well.  ...  The idea of parallelizing the operations was found in classical cellular automata. However, how to translate cellular automata into a quantum mechanical framework turned out not to be trivial.  ... 
arXiv:0808.0679v1 fatcat:3n6hwddb7rhflenqcxmmalh7wy

Cellular Automata based Artificial Financial Market [chapter]

Jingyuan Ding
2011 Cellular Automata - Simplicity Behind Complexity  
As a result, the cellular automaton (CA) is adopted. Classical CA is a kind of large scale discrete dynamical systems.  ...  It is not a perfect model to get a new capital theory, but we can still realize how cellular automata can help us to do research in financial area. Cellular Automata based Artificial  ...  The classic cellular automata based capital market model Recent years, the non public information's influence on capital market came into researchers' sights.  ... 
doi:10.5772/15805 fatcat:63hx5qrmq5cwvcj5s77zmu7mp4

Gauge-invariance in cellular automata [article]

Pablo Arrighi, Giuseppe Di Molfetta, Nathanaël Eon
2020 arXiv   pre-print
A step-by-step gauging procedure to enforce this symmetry upon a given Cellular Automaton is developed, and three examples of gauge-invariant Cellular Automata are examined.  ...  In this paper, we provide discrete counterparts to the main gauge theoretical concepts directly in terms of Cellular Automata.  ...  efficiently simulate interacting fundamental particles theories-a task which would take a very long time on classical computers.  ... 
arXiv:2004.03656v1 fatcat:qzlmmte5bzeopausmibs5susg4

Quantumness of discrete Hamiltonian cellular automata

Hans-Thomas Elze, S. Varró, P. Ádám, T.S. Biró, G.G. Barnaföldi, P. Lévai
2014 EPJ Web of Conferences  
We summarize a recent study of discrete (integer-valued) Hamiltonian cellular automata (CA) showing that their dynamics can only be consistently defined, if it is linear in the same sense as unitary evolution  ...  This allows to construct an invertible map between such CA and continuous quantum mechanical models, which incorporate a fundamental scale.  ...  Introduction The Cellular Automaton Interpretation of quantum mechanics has recently been laid out by G. 't Hooft [1] .  ... 
doi:10.1051/epjconf/20147802005 fatcat:3lz3g7f2mzgrbdcfpy23wfzwsu

Computational classification of cellular automata

Klaus Sutner
2012 International Journal of General Systems  
We discuss attempts at the classification of cellular automata, in particular with a view towards decidability.  ...  Even in the decidable case, computational hardness poses a major obstacle for the automatic analysis of cellular automata.  ...  Cellular automata were originally developed by von Neumann, with help from Ulam, to give a precise solution to the problem of self-reproduction, see Neumann (1966) .  ... 
doi:10.1080/03081079.2012.695899 fatcat:sebvk4v4v5hblkb3gjwgcxu5ku

Local unitary quantum cellular automata

Carlos A. Pérez-Delgado, Donny Cheung
2007 Physical Review A. Atomic, Molecular, and Optical Physics  
In this paper we present a quantization of Cellular Automata.  ...  Some results that show the benefits of basing the model on local unitary operators are shown: universality, strong connections to the circuit model, simple implementation on quantum hardware, and a wealth  ...  Acknowledgments The authors would like to thank Niel de Beaudrap and John Watrous for their invaluable comments on preliminary versions of this paper.  ... 
doi:10.1103/physreva.76.032320 fatcat:lrdqythurzb7vnojyz5hrcwone

Quantum features of natural cellular automata

Hans-Thomas Elze
2016 Journal of Physics, Conference Series  
They can be mapped reversibly to continuum models by applying Sampling Theory.  ...  The class of "natural" Hamiltonian cellular automata is based exclusively on integer-valued variables and couplings and their dynamics derives from an Action Principle.  ...  Acknowledgments It is a pleasure to thank G. Grössing and J. Walleczek for the kind invitation to the conference "Emergent Quantum Mechanics" (Vienna, October 2015) and H. Batelaan, A. Caticha and G.  ... 
doi:10.1088/1742-6596/701/1/012017 fatcat:k2eb77xqnbdabfmxsvjjrdqtau

Binary Adders on Quantum-Dot Cellular Automata

Ismo Hänninen, Jarmo Takala
2008 Journal of Signal Processing Systems  
This article describes the design of adder units on quantum-dot cellular automata (QCA) nanotechnology, which promises very dense circuits and high operating frequencies, using a single homogeneous layer  ...  Our designs occupy only a fraction of area compared to the previous noise rejecting design, while having also superior performance, and it is shown that the wiring overhead of the arithmetic circuits on  ...  In addition, the authors thank the anonymous reviewers for their constructive comments to improve this paper.  ... 
doi:10.1007/s11265-008-0284-5 fatcat:3ro6hm3nynba5hrfsffjzaok7a

An overview of Quantum Cellular Automata [article]

Pablo Arrighi
2019 arXiv   pre-print
Quantum cellular automata consist in arrays of identical finite-dimensional quantum systems, evolving in discrete-time steps by iterating a unitary operator G.  ...  Quantum cellular automata provide a model/architecture for distributed quantum computation. More generally, they encompass most of discrete-space discrete-time quantum theory.  ...  I would like to thank Jarkko Kari and Grzegorz Rozenberg for inviting me to write this overview, a task which I had been postponing for too long.  ... 
arXiv:1904.12956v2 fatcat:fs3m6tudibe7vdz7d4onzj4d3m

A Survey of Cellular Automata: Types, Dynamics, Non-uniformity and Applications [article]

Kamalika Bhattacharjee, Nazma Naskar, Souvik Roy, Sukanta Das
2018 arXiv   pre-print
Cellular automata (CAs) are dynamical systems which exhibit complex global behavior from simple local interaction and computation.  ...  In this survey, we tour to the various types of CAs introduced till date, the different characterization tools, the global behaviors of CAs, like universality, reversibility, dynamics etc.  ...  Acknowledgements The authors gratefully acknowledge the anonymous reviewers for their comments and suggestions, which have helped to improve the quality and readability of the paper.  ... 
arXiv:1607.02291v3 fatcat:nvvcvjlupvdtpdz34kii2ovt5m
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