Quantum Computation of the WRT-TQFT Partition Function

par William Mistegård (Univ. of Southern Denmark)

mercredi 13 mai 2026, 10:30 → 11:30 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Seed Seminar of Mathematics and Physics

Spring '26: TQFT and Knot Theory 

Quantum Computation is a new paradigm for computation in which data is stored in quantum systems, processed via physical manipulations (unitary gates) of these systems and finally read out using measurements. Theoretically, this gives an exponential speed-up over classical computing for important problems including simulations of quantum many body physics. Recent years have witnessed an acceleration in the development of hardware for quantum computers. One challenge is to make these robust against noise, i.e. unwarranted interactions with the computer’s environment, which may cause computational errors. There are known schemes to overcome this problem and achieve universal fault-tolerant quantum computing.

One of the most powerful software schemes for fault-tolerant quantum computing is through so-called topological quantum error correction. This is deeply connected to topological quantum field theories (TQFT), which are quantum field theories 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 be topologically protected – i.e. there is a low probability that noise from the environment will alter the topology of the system/processes and thereby introduce errors.

In this talk, I will survey some of the deep connections between TQFT and Quantum Computing. I will also present details of 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 topology. This project is further motivated by a BQP-completeness essentially result due to Freedman, Larsen, Kitaev and Wang, which asserts that any problem which can be efficiently solved by a quantum computer can be reduced (with polynomial overhead) to the computation of the WRT-TQFT partition function.

This project is joint with the following colleagues at Centre for Quantum Mathematics at University of Southern Denmark: J.E. Andersen, S. Hindson, G.K. Potter and K. Wernli.

More information: https://seedseminar.apps.math.cnrs.fr/program/#may-13-2026

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