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SUMMARY:Quantum Computation of the WRT-TQFT Partition Function
DTSTART:20260513T083000Z
DTEND:20260513T093000Z
DTSTAMP:20260509T130000Z
UID:indico-event-16320@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: William Mistegård (Univ. of Southern Denmark)\n\nSe
 ed Seminar of Mathematics and Physics\nSpring '26: TQFT and Knot Theory \
 nQuantum Computation is a new paradigm for computation in which data is st
 ored in quantum systems\, processed via physical manipulations (unitary ga
 tes) of these systems and finally read out using measurements. Theoretical
 ly\, this gives an exponential speed-up over classical computing for impor
 tant problems including simulations of quantum many body physics. Recent y
 ears have witnessed an acceleration in the development of hardware for qua
 ntum computers. One challenge is to make these robust against noise\, i.e.
  unwarranted interactions with the computer’s environment\, which may ca
 use computational errors. There are known schemes to overcome this problem
  and achieve universal fault-tolerant quantum computing.\nOne of the most 
 powerful software schemes for fault-tolerant quantum computing is through 
 so-called topological quantum error correction. This is deeply connected t
 o topological quantum field theories (TQFT)\, which are quantum field theo
 ries that are invariant under diffeomorphisms of space-time. There is also
  an ongoing effort to build hardware based on topological phases of matter
  (described by TQFT in the low-energy regime)\, as such a computer would b
 e topologically protected – i.e. there is a low probability that noise f
 rom the environment will alter the topology of the system/processes and th
 ereby introduce errors.\nIn this talk\, I will survey some of the deep con
 nections between TQFT and Quantum Computing. I will also present details o
 f an ongoing project\, which aims to use quantum computing to approximate 
 the Witten-Reshetikhin-Turaev TQFT partition function of a general closed 
 three-manifold with the goal of probing central conjectures in quantum top
 ology. This project is further motivated by a BQP-completeness essentially
  result due to Freedman\, Larsen\, Kitaev and Wang\, which asserts that an
 y problem which can be efficiently solved by a quantum computer can be red
 uced (with polynomial overhead) to the computation of the WRT-TQFT partiti
 on function.\nThis project is joint with the following colleagues at Centr
 e for Quantum Mathematics at University of Southern Denmark: J.E. Andersen
 \, S. Hindson\, G.K. Potter and K. Wernli.\nMore information: https://seed
 seminar.apps.math.cnrs.fr/program/#may-13-2026\n========\nPour être infor
 mé des prochains séminaires vous pouvez vous abonner à la liste de diff
 usion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: 
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  et nom) et laissez le corps du message vide.\n\nhttps://indico.math.cnrs.
 fr/event/16320/
LOCATION:Centre de conférences Marilyn et James Simons (IHES)
URL:https://indico.math.cnrs.fr/event/16320/
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