Quantum Representations of MCGs and Their Applications to Quantum Computing
eScholarship, University of California, 2019
Online
unknown
We explore how skein theoretic techniques can be applied to the study of quantumrepresentations of mapping class groups. Of particular interest will be looking into theasymptotic faithfulness property of quantum representations coming from unimodal versionsof representation categories of quantum groups. We then introduce a combinatorialproperty on the graphical calculus of these representation categories which implies asymptoticfaithfulness. We proceed to show that this property is satisfied in some specific cases,in short we provide support for the conjecture that these quantum representations willalways be asymptotically faithful. This will lead into a discussion of other applicationswithin low dimensional topology. Finally applications to topological quantum computingwill be given, introducing a potential encoding of qudits making use of these quantumrepresentations.
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Quantum Representations of MCGs and Their Applications to Quantum Computing
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Autor/in / Beteiligte Person: | Bloomquist, Wade |
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Veröffentlichung: | eScholarship, University of California, 2019 |
Medientyp: | unknown |
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