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Reversible quantum cellular automata
[article]
2004
arXiv
pre-print
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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]
2019
arXiv
pre-print
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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
2011
Theoretical Computer Science
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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]
2018
arXiv
pre-print
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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
2021
IEEE Access
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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]
2008
arXiv
pre-print
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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]
2011
Cellular Automata - Simplicity Behind Complexity
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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. www.intechopen.com 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]
2020
arXiv
pre-print
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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
2014
EPJ Web of Conferences
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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
2012
International Journal of General Systems
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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
2007
Physical Review A. Atomic, Molecular, and Optical Physics
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2007 pre-print arXiv:0709.0006v1 fatcat:e6yxoji4anbarblz4fs3d2zsk4
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
2016
Journal of Physics, Conference Series
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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
2008
Journal of Signal Processing Systems
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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]
2019
arXiv
pre-print
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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]
2018
arXiv
pre-print
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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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