TY  - JOUR
A1  - Gross, David
A1  - Nesme, V.
A1  - Vogts, H.
A1  - Werner, Reinhard F.
T1  - Index theory of one dimensional quantum walks and cellular automata
JF  - Communications in mathematical physics
N2  - If a one-dimensional quantum lattice system is subject to one step of a reversible discrete-time dynamics, it is intuitive that as much "quantum information" as moves into any given block of cells from the left, has to exit that block to the right. 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 the system. The index supplies a complete characterization of two properties of the discrete dynamics. First, two systems S-1, S-2 can be "pieced together", in the sense that there is a system S which acts like S-1 in one region and like S-2 in some other region, if and only if S-1 and S-2 have the same index. Second, the index labels connected components of such systems: equality of the index is necessary and sufficient for the existence of a continuous deformation of S-1 into S-2. In the case of quantum walks, the index is integer-valued, whereas for cellular automata, it takes values in the group of positive rationals. In both cases, the map S bar right arrow. ind S is a group homomorphism if composition of the discrete dynamics is taken as the group law of the quantum systems. Systems with trivial index are precisely those which can be realized by partitioned unitaries, and the prototypes of systems with non-trivial index are shifts.
Y1  - 2012
U6  - https://doi.org/10.1007/s00220-012-1423-1
SN  - 0010-3616
VL  - 310
IS  - 2
SP  - 419
EP  - 454
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Guetschow, Johannes
A1  - Nesme, Vincent
A1  - Werner, Reinhard F.
T1  - Self-similarity of cellular automata on abelian groups
JF  - Journal of cellular automata
N2  - It is well known that the spacetime diagrams of some cellular automata have a self-similar fractal structure: for instance Wolfram's rule 90 generates a Sierpinski triangle. Explaining the self-similarity of the spacetime diagrams of cellular automata is a well-explored topic, but virtually all of the results revolve around a special class of automata, whose typical features include irreversibility, an alphabet with a ring structure, a global evolution that is a ring homomorphism, and a property known as (weakly) p-Fermat. The class of automata that we study in this article has none of these properties. Their cell structure is weaker, as it does not come with a multiplication, and they are far from being p-Fermat, even weakly. However, they do produce self-similar spacetime diagrams, and we explain why and how.
KW  - fractal
KW  - abelian group
KW  - linear cellular automaton
KW  - substitution system
KW  - self-similarity
Y1  - 2012
SN  - 1557-5969
VL  - 7
IS  - 2
SP  - 83
EP  - 113
PB  - Old City Publishing Science
CY  - Philadelphia
ER  - 
TY  - JOUR
A1  - Arrighi, Pablo
A1  - Nesme, Vincent
A1  - Werner, Reinhard F.
T1  - One-Dimensional quantum cellular automata
JF  - International journal of unconventional computing : non-classical computation and cellular automata
N2  - We define and study quantum cellular automata (QCA). We show that they are reversible and that the neighborhood of the inverse is the opposite of the neighborhood. We also show that QCA always admit, modulo shifts, a two-layered block representation. Note that the same two-layered block representation result applies also over infinite configurations, as was previously shown for one-dimensional systems in the more elaborate formalism of operators algebras [18]. Here the proof is simpler and self-contained, moreover we discuss a counterexample QCA in higher dimensions.
KW  - cellular automata
KW  - quantum
KW  - neighborhood
KW  - block representation
Y1  - 2011
SN  - 1548-7199
VL  - 7
IS  - 4
SP  - 223
EP  - 244
PB  - Old City Publishing Science
CY  - Philadelphia
ER  - 
TY  - JOUR
A1  - Zoller, Peter
A1  - Beth, Thomas
A1  - Binosi, D.
A1  - Blatt, Rainer
A1  - Briegel, Hans J.
A1  - Bruss, D.
A1  - Calarco, Tommaso
A1  - Cirac, Juan Ignacio
A1  - Deutsch, David
A1  - Eisert, Jens
A1  - Ekert, Artur
A1  - Fabre, Claude
A1  - Gisin, Nicolas
A1  - Grangiere, P.
A1  - Grassl, Markus
A1  - Haroche, Serge
A1  - Imamoglu, Atac
A1  - Karlson, A.
A1  - Kempe, Julia
A1  - Kouwenhoven, Leo P.
A1  - Kröll, S.
A1  - Leuchs, Gerd
A1  - Lewenstein, Maciej
A1  - Loss, Daniel
A1  - Lütkenhaus, Norbert
A1  - Massar, Serge
A1  - Mooij, J. E.
A1  - Plenio, Martin Bodo
A1  - Polzik, Eugene
A1  - Popescu, Sandu
A1  - Rempe, Gerhard
A1  - Sergienko, Alexander
A1  - Suter, David
A1  - Twamley, John
A1  - Wendin, Göran
A1  - Werner, Reinhard F.
A1  - Winter, Andreas
A1  - Wrachtrup, Jörg
A1  - Zeilinger, Anton
T1  - Quantum information processing and communication : Strategic report on current status, visions and goals for research in Europe
N2  - We present an excerpt of the document "Quantum Information Processing and Communication: Strategic report on current status, visions and goals for research in Europe", which has been recently published in electronic form at the website of FET (the Future and Emerging Technologies Unit of the Directorate General Information Society of the European Commission, http://www.cordis.lu/ist/fet/qipc-sr.htm). This document has been elaborated, following a former suggestion by FET, by a committee of QIPC scientists to provide input towards the European Commission for the preparation of the Seventh Framework Program. Besides being a document addressed to policy makers and funding agencies (both at the European and national level), the document contains a detailed scientific assessment of the state-of-the-art, main research goals, challenges, strengths, weaknesses, visions and perspectives of all the most relevant QIPC sub-fields, that we report here
Y1  - 2005
SN  - 1434-6060
ER  -