A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Filters
Quantum automata and algebraic groups
2005
Journal of symbolic computation
Preserved Fulltext
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]
2008
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
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]
2003
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
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
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
(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]
2012
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
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]
1995
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
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
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
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
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
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
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
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
2005
SIAM journal on computing (Print)
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
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
2012
Communications in Mathematical Physics
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
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
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
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
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
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
1978
Bulletin of the American Mathematical Society
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
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
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
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