NDLI: Topology, Formal Languages and Quantum Information

Content Provider	Springer Nature Link
Author	Rasetti, Mario
Copyright Year	2010
Abstract	The paper provides a critical overview of the basic conceptual tools and algorithms of quantum information theory underlying the construction of quantum invariants of links and 3-manifolds as well as of their connections with algorithms and algorithmic complexity questions that arise in geometry and quantum gravity models.Moreover, it argues that such quantum information manipulation tools may allow us to explore much wider fields than mere computation, reaching beyond its boundaries to touch the very roots of the universal structure of formal languages. The paper addresses just a few among the many technical details necessary to pursue the general argument, its main aim being to show how a complex blend of notions coming from formal language theory, finite group theory, and quantum information theory do indeed lead to a novel perspective in the science of languages.The quantum algorithm on which the whole structure discussed is grounded is the quantum automaton recently designed (Marzuoli, Rasetti, Garnerone) to construct an efficient additive approximation of link and 3-manifold topological invariants in the framework of SU (2) Chern-Simons-Witten topological quantum field theory at finite values of the coupling constant k. The model of computation adopted in it is the q-deformed spin network model viewed as a quantum recognizer, where each basic unitary transition function can be efficiently processed by a standard quantum circuit.
Ending Page	317
Page Count	29
Starting Page	289
File Format	PDF
ISSN	14249286
e-ISSN	14249294
Journal	Milan Journal of Mathematics
Issue Number	1
Volume Number	78
Language	English
Publisher	SP Birkhäuser Verlag Basel
Publisher Date	2010-03-25
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Quantum computation topological quantum field theory Topological invariants Analysis Formal languages and automata Quantum algorithms and complexity Mathematics formal language theory quantum information topological invariants of links and 3-manifolds
Content Type	Text
Resource Type	Article
Subject	Mathematics

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