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3.3
Journals
Quantum Reports
Special Issues
Groups, Geometry and Topology for Quantum Computations
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Groups, Geometry and Topology for Quantum Computations

A special issue of Quantum Reports (ISSN 2624-960X).

Deadline for manuscript submissions: closed (31 August 2021) | Viewed by 8119

Special Issue Editor

Prof. Dr. Michel Planat

E-Mail Website
Guest Editor
Institut FEMTO-ST, 15B Avenue des Montboucons, 25000 Besançon, France
Interests: Physics: quantum computing, quantum information, signal processing, mathematical physics; Mathematics: group theory, knot theory, discrete mathematics, graph theory, number theory, finite geomety

Special Issue Information

Dear Colleagues,

In recent work pertaining to digital quantum computations—the quantum parallel to classical computations—algebraic concepts are being introduced as a resource. This goes from an extensive use of group theory (finite groups such as Paulis and Cliffords, free groups with relations, group covariance in generalized quantum measurements, etc.), of geometry (e.g., finite geometries for modeling quantum commutation, entanglement, and contextuality) and of topology for adapting quantum error correction to nonlocality. Further, topological order and braids are being investigated for quantum computing in 2D (in anyons) and in 3D (with 3-manifolds).

We welcome papers in the aforementioned and related areas.

Prof. Dr. Michel Planat
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

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. Quantum Reports is an international peer-reviewed open access quarterly 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 1400 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

  • Group theory and quantum contextuality
  • Magic states
  • MICs: minimal informationally complete POVMs
  • Projective and hyperbolic geometry
  • Geometry and entanglement
  • Topological quantum computation
  • Topological order, tensor networks, bulk/boundary correspondence
  • Knots, links, and braids
  • Low-dimensional manifolds

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Published Papers (2 papers)

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13 pages, 463 KiB  
Article
Topological Quantum Computing and 3-Manifolds
by Torsten Asselmeyer-Maluga
Quantum Rep. 2021, 3(1), 153-165; https://doi.org/10.3390/quantum3010009 - 5 Feb 2021
Cited by 4 | Viewed by 4129
Abstract
In this paper, we will present some ideas to use 3D topology for quantum computing. Topological quantum computing in the usual sense works with an encoding of information as knotted quantum states of topological phases of matter, thus being locked into topology to [...] Read more.
In this paper, we will present some ideas to use 3D topology for quantum computing. Topological quantum computing in the usual sense works with an encoding of information as knotted quantum states of topological phases of matter, thus being locked into topology to prevent decay. Today, the basic structure is a 2D system to realize anyons with braiding operations. From the topological point of view, we have to deal with surface topology. However, usual materials are 3D objects. Possible topologies for these objects can be more complex than surfaces. From the topological point of view, Thurston’s geometrization theorem gives the main description of 3-dimensional manifolds. Here, complements of knots do play a prominent role and are in principle the main parts to understand 3-manifold topology. For that purpose, we will construct a quantum system on the complements of a knot in the 3-sphere. The whole system depends strongly on the topology of this complement, which is determined by non-contractible, closed curves. Every curve gives a contribution to the quantum states by a phase (Berry phase). Therefore, the quantum states can be manipulated by using the knot group (fundamental group of the knot complement). The universality of these operations was already showed by M. Planat et al. Full article
(This article belongs to the Special Issue Groups, Geometry and Topology for Quantum Computations)
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12 pages, 817 KiB  
Article
Finite Groups for the Kummer Surface: The Genetic Code and a Quantum Gravity Analogy
by Michel Planat, David Chester, Raymond Aschheim, Marcelo M. Amaral, Fang Fang and Klee Irwin
Quantum Rep. 2021, 3(1), 68-79; https://doi.org/10.3390/quantum3010005 - 25 Jan 2021
Cited by 6 | Viewed by 3352
Abstract
The Kummer surface was constructed in 1864. It corresponds to the desingularization of the quotient of a 4-torus by 16 complex double points. Kummer surface is known to play a role in some models of quantum gravity. Following our recent model of the [...] Read more.
The Kummer surface was constructed in 1864. It corresponds to the desingularization of the quotient of a 4-torus by 16 complex double points. Kummer surface is known to play a role in some models of quantum gravity. Following our recent model of the DNA genetic code based on the irreducible characters of the finite group G5:=(240,105)≅Z5⋊2O (with 2O the binary octahedral group), we now find that groups G6:=(288,69)≅Z6⋊2O and G7:=(336,118)≅Z7⋊2O can be used as models of the symmetries in hexamer and heptamer proteins playing a vital role for some biological functions. Groups G6 and G7 are found to involve the Kummer surface in the structure of their character table. An analogy between quantum gravity and DNA/RNA packings is suggested. Full article
(This article belongs to the Special Issue Groups, Geometry and Topology for Quantum Computations)
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