Topological Aspects of Quantum Gravity and Quantum Information Theory

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: 30 September 2024 | Viewed by 3558

Special Issue Editors


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Guest Editor
FSE and FBL, University of Saint Joseph, Estrada Marginal da Ilha Verde, 14-17, Macao, China
Interests: quantum field theory and symmetry; condensed matter systems; quantum information
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Guest Editor
Institut für Didaktik der Physik, Universität Münster, 48149 Münster, Germany
Interests: physics education; quantum physics; gauge symmetry

Special Issue Information

Dear Colleagues, 

Both in the field of quantum gravity and in quantum information theory, the importance of topology is increasing. The discovery of topological phases of matter, together with the existence of analogue systems of gravity and their evident relation to quantum information, bring interesting scenarios where important discoveries will appear. 

As first proposed by Andrei Sakharov in 1967, gravity as we experience it in real life might emerge as a mean field approximation of underlying microscopic degrees of freedom of a quantum field theory. It is also possible that some unexplained aspects of gravity might emerge as a collective effect originally from microscopic degrees of freedom.

The most evident connection between gravity and quantum information can be visualized through the physics of black holes where the area of the event horizon measures the amount of information hidden behind it. The Hawking radiation and its associated thermality bring as a consequence the existence of the famous black hole information paradox discovered by Hawking in his seminal papers on the subject.

In addition, the proved connections between the physics of black holes and some condensed matter systems bring scenarios where quantum information can be analyzed from the perspective of condensed matter systems and subsequently mapped to gravitational systems for a deeper understanding of gravity.  

Furthermore, deep relations between entanglement and the Einstein field equation have been explored by many authors, such as the ER=EPR correspondence proposed by Suskind and Maldacena in relation to the AdS/CFT duality.

In this sense, understanding topological aspects in gravity might have a direct relation to topological aspects in related field theories as well as in condensed matter systems. These important subjects will be explored in this Special Issue.

This Special Issue invites contributions reporting progress related to topological aspects both in the field of quantum gravity and in quantum information theory. Moreover, contributions focusing on suitable pedagogical introductions and model building related to existing theories are welcome.

Submit your paper and select the Journal “Symmetry” and the Special Issue “Topological Aspects of Quantum Gravity and Quantum Information Theory” via: MDPI submission system. Our papers will be published on a rolling basis and we will be pleased to receive your submission once you have finished it.

Dr. Ivan Arraut
Prof. Dr. Stefan Heusler
Guest Editors

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • quantum gravity
  • quantum information
  • entanglement
  • black holes
  • information paradox
  • ER=EPR conjecture
  • model building
  • condensed matter physics
  • topological phase transitions
  • AdS/CFT correspondence

Published Papers (1 paper)

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Research

10 pages, 888 KiB  
Article
Character Varieties and Algebraic Surfaces for the Topology of Quantum Computing
by Michel Planat, Marcelo M. Amaral, Fang Fang, David Chester, Raymond Aschheim and Klee Irwin
Symmetry 2022, 14(5), 915; https://doi.org/10.3390/sym14050915 - 30 Apr 2022
Cited by 5 | Viewed by 2672
Abstract
It is shown that the representation theory of some finitely presented groups thanks to their SL2(C) character variety is related to algebraic surfaces. We make use of the Enriques–Kodaira classification of algebraic surfaces and related topological tools to [...] Read more.
It is shown that the representation theory of some finitely presented groups thanks to their SL2(C) character variety is related to algebraic surfaces. We make use of the Enriques–Kodaira classification of algebraic surfaces and related topological tools to make such surfaces explicit. We study the connection of SL2(C) character varieties to topological quantum computing (TQC) as an alternative to the concept of anyons. The Hopf link H, whose character variety is a Del Pezzo surface fH (the trace of the commutator), is the kernel of our view of TQC. Qutrit and two-qubit magic state computing, derived from the trefoil knot in our previous work, may be seen as TQC from the Hopf link. The character variety of some two-generator Bianchi groups, as well as that of the fundamental group for the singular fibers E˜6 and D˜4 contain fH. A surface birationally equivalent to a K3 surface is another compound of their character varieties. Full article
(This article belongs to the Special Issue Topological Aspects of Quantum Gravity and Quantum Information Theory)
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