''It’s the Symmetry, Stupid!'' Gearing Up Tensor Networks for the Topological Quantum Revolution

01 December 2023 → 30 November 2028
European funding: framework programme
Research disciplines
  • Natural sciences
    • Algebraic structures in mathematical physics
Other information
Project description

This proposal is set in the era of the second quantum revolution, in which there is a strong need for a computational framework to
describe and simulate topological materials and quantum devices possessing exotic particle statistics.
* The two leading actors: symmetries and tensor networks.
* The story: while the topological materials seem to defy Landau’s symmetry breaking paradigm as they do not exhibit a local order
parameter, tensor networks strike back with the emergence of a local “pulling-through” symmetry of the local tensors describing
* The catch: the symmetry happens in the shadow world of entanglement degrees of freedom, is in general non-invertible, and
speaks the language of bimodule categories.
* The magic: the tensor network picture makes the abstract concepts and mathematical tools needed to describe topological and
critical systems, such as cohomology theory and bimodule categories, very tangible and concrete as wavefunctions of quantum spin
systems which can easily be put on a computer.
* The mission: develop the mathematics of tensor network representations of (higher) categorical and non-invertible symmetries;
construct a computational toolbox which exploits those symmetries; construct explicit matrix product operator intertwiners for
dualities between theories with non-Abelian / categorical symmetries; construct novel CFTs from categorical data; create a bridge
between bimodule categories and integrability.
* The crescendo: tensor networks with categorical symmetries take over the world by 1. setting up real-space renormalization group
flows in which unwanted relevant perturbations are crushed and 2.constructing and evaluating quantum error correcting codes
based on non-Abelian anyons.
* The take-away: deep theoretical ideas and state of the art computational aspects are not parallel lines of development, but are one
and the same and must be fused with each other.
* The moral: For things to remain the same, everything must change.
Remaining characters 4
Has this proposal (or a very similar one) been submitted in the past 2 y

Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency (ERCEA). Neither the European Union nor the authority can be held responsible for them.