Filters








5,033 Hits in 5.0 sec

Quantum automata and algebraic groups

Harm Derksen, Emmanuel Jeandel, Pascal Koiran
2005 Journal of symbolic computation  
We show that several problems which are known to be undecidable for probabilistic automata become decidable for quantum finite automata.  ...  Our main tool is an algebraic result of independent interest: we give an algorithm which, given a finite number of invertible matrices, computes the Zariski closure of the group generated by these matrices  ...  Acknowledgments P.K. would like to thank Etienne Ghys for pointing out Onishchik and Vinberg (1990) . The main algorithm was inspired by discussions with Joris van der Hoeven.  ... 
doi:10.1016/j.jsc.2004.11.008 fatcat:5gdqdl25vrdaxabg37r5nxewl4

Remarks on the structure of Clifford quantum cellular automata [article]

Dirk-Michael Schlingemann
2008 arXiv   pre-print
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.  ...  Quantum cellular automata provide model for analyzing quantum computational processes and quantum computational complexity.  ... 
arXiv:0812.0714v1 fatcat:choo33d77vcj5px5khikpiua5i

Decidable and undecidable problems about quantum automata [article]

Vincent D. Blondel, Emmanuel Jeandel, Pascal Koiran, Natacha Portier
2003 arXiv   pre-print
This result is in contrast with the corresponding situation for probabilistic finite automata for which it is known that strict and non-strict thresholds both lead to undecidable problems.  ...  We study the following decision problem: is the language recognized by a quantum finite automaton empty or non-empty?  ...  For the proof we use the fact that any compact matrix group is algebraic and the group we consider can be given an effective description.  ... 
arXiv:quant-ph/0304082v1 fatcat:ofivd7nigjfj5ng66fvtkf75ym

Page 7608 of Mathematical Reviews Vol. , Issue 2002J [page]

2002 Mathematical Reviews  
(quantum) automata.  ...  2002):8 1005 81 is centred around the so-called history group (the analogue of the Heisenberg-Weyl group in the present framework) and its repre- sentations.  ... 

Algebraic Characterization of the Class of Languages recognized by Measure Only Quantum Automata [article]

Carlo Comin, Maria Paola Bianchi
2012 arXiv   pre-print
We study a model of one-way quantum automaton where only measurement operations are allowed (MOn-1qfa).  ...  We give an algebraic characterization of LMO, showing that the syntactic monoids of the languages in LMO are exactly the literal pseudovariety of J-trivial literally idempotent monoids, where J is the  ...  This class of automata has been fully characterized algebraically in [1] as the class of automata recognizing exactly regular languages having syntactic monoids in the class BG of block groups.  ... 
arXiv:1206.1702v2 fatcat:nzq3ppcprrc6zhqvlomdh3cmwu

Hybrid systems and quantum automata: Preliminary announcement [chapter]

R. L. Grossman, M. Sweedler
1995 Lecture Notes in Computer Science  
Finite automata and input-output systems are concerned with commutative R, while quantum systems, such as quantum automata, are concerned with non-commutative R arising from Hermitian operators on the  ...  In this paper, we present a number of examples of hybrid systems and quantum automata and point out some relationships between them.  ...  Quantum automata and languages Algebra of input events. Consider a language defined over an input alphabet Ω.  ... 
doi:10.1007/3-540-60472-3_10 fatcat:lx3z7zidwjfvddiknyw7khpvtu

Page 150 of Mathematical Reviews Vol. , Issue 2002A [page]

2002 Mathematical Reviews  
Mo- tivated by these observations, the authors formulate a class of cellular automata directly in terms of crystals of irreducible finite- dimensional representations of quantum affine algebras U'(g, and  ...  After recalling some facts about quantum groups, it is shown that the problem of constructing a U;(g)-invariant quantization ; equivalent to the problem of constructing a U(g)-invariant and U(g){[A])  ... 

Page 2900 of Mathematical Reviews Vol. , Issue 92e [page]

1992 Mathematical Reviews  
Since this algebra underlies the noncompact group SU(1,1), we are thus able to define unambiguously the dynamical group related to the generalized quantum oscillator.  ...  ) Group-theoretical approach to the classical and quantum oscillator with time-dependent mass and frequency.  ... 

Page 2366 of Mathematical Reviews Vol. , Issue 93d [page]

1993 Mathematical Reviews  
Groups Random Surfaces and 2D Quantum Gravity ...  ...  on General Topology and Applications Topology Symposium, Tsukuba Progress in Mathematics, 97 Providence, RI, 1988 Pushchino, 1990 Quantum groups Quantum logics, Part 1 Quantum logics, Part 2 Quantum mechanics  ... 

Decidable and Undecidable Problems about Quantum Automata

Vincent D. Blondel, Emmanuel Jeandel, Pascal Koiran, Natacha Portier
2005 SIAM journal on computing (Print)  
This result is in contrast with the corresponding situation for probabilistic finite automata, for which it is known that strict and nonstrict thresholds both lead to undecidable problems.  ...  We study the following decision problem: is the language recognized by a quantum finite automaton empty or nonempty?  ...  For the proof we use the fact that any compact matrix group is algebraic, and the group we consider can be given an effective description. Complex versus real entries.  ... 
doi:10.1137/s0097539703425861 fatcat:yy7c734d3rhczm2zvgse7ytcdy

Index Theory of One Dimensional Quantum Walks and Cellular Automata

D. Gross, V. Nesme, H. Vogts, R. F. Werner
2012 Communications in Mathematical Physics  
In the case of quantum walks, the index is integer-valued, whereas for cellular automata, it takes values in the group of positive rationals.  ...  For two types of such systems - namely quantum walks and cellular automata - we make this intuition precise by defining an index, a quantity that measures the "net flow of quantum information" through  ...  We gratefully acknowledge the support of the DFG (Forschergruppe 635) and the EU (projects CORNER and QUICS), as well as the Erwin Schrödinger Institute.  ... 
doi:10.1007/s00220-012-1423-1 fatcat:crdsr5posfamrbkqpmjnidpemi

Page 4933 of Mathematical Reviews Vol. , Issue 94h [page]

1994 Mathematical Reviews  
of algebras and their representations Quasicrystals: the state of the art Ramat-Gan, 1991/1992 Recent advances in real algebraic geometry and quadratic Rehovot, 1991/1992 Representation theory of groups  ...  .. * 86002 Computational Crystal Growers, Geometry Center Quantum Deformations of Algebras and their Representations Rough Sets—State of the Art and Perspectives, Ist International  ... 

Page 3510 of Mathematical Reviews Vol. , Issue 93f [page]

1993 Mathematical Reviews  
methods in quantum field theories .... * 81007 Tree automata and languages * 68007 Trees and hierarchical structures * 92004 Trieste, 1990 * 81007 Turbulence and stochastic processes: Kolmogorov’s ideas  ...  Models Representation Theory of Lie Groups and its Applications, 3rd ED isis ivcvcssdpiowndscvccrvvedscs ; Tree Languages and Tree Automata Yokohama, 1992  ... 

Book Review: Grundzüge der universellen Algebra

P. M. Cohn
1978 Bulletin of the American Mathematical Society  
In recent years probabilistic techniques have played a large role in constructive quantum field theory, but the random fields have been constructed on Euclidean space, rather than Minkowski space, and  ...  the results for quantum fields have been obtained by analytic continuation.  ...  A third chapter lists examples: groupoids, groups, rings, lattices and Boolean algebras.  ... 
doi:10.1090/s0002-9904-1978-14434-6 fatcat:ybgcqovj7rfdje3wgecdngjbxy

Page 8742 of Mathematical Reviews Vol. , Issue 2003k [page]

2003 Mathematical Reviews  
By means of the crystal base theory, we study a class of such automata associated with the quantum affine algebra U,(g,,) for the nonexceptional series g, = Pd we .C}"’, Dh’ and p..  ...  (RS-MURE; Moscow) Unitary representations of the quantum Lorentz group, and the quantum relativistic Toda chain. (Russian. Russian summary) Teoret. Mat.  ... 
« Previous Showing results 1 — 15 out of 5,033 results