Sayan Chakraborty
From Noncommutative Tori to Hybrid Quantum Codes
Quantum error correction is essential for building reliable quantum technologies. In this talk, we explore how ideas from lattices, operator algebras, and noncommutative tori help protect quantum information, starting from well-known constructions such as GKP codes. We then introduce a unified mathematical framework that connects continuous and discrete quantum systems, leading to new “hybrid” codes. This is joint work with Victor V. Albert.
Roberto Conti
Towards a definition of the Fourier-Stieltjes algebra of a Fell bundle
It will be a honour for me to celebrate Erik’s 70th birthday on this occasion. Our scientific collaboration started back at the end of the 90s and continued steadily without significant interruptions until the present days. I will present an overview of our recent work on Fell bundles and positive definite bundle maps , highlighting their connection with our previous work on the Fourier-Stieltjes algebra of a (unital, discrete, twisted) C*-dynamical system.
Jonas Eidesen
Projective error models
By defining projective error models we study the mathematical structure of Clifford codes and stabilizer codes using tools from projective representation theory. These are two classes of quantum codes that have been well studied in the last couple of decades. We show that the obstruction for a stabilizer code to be non-trivial is given by a class in group cohomologyl. In the case where the projective error model corresponds to a nice error basis we give a complete characterization of when a Clifford code is a stabilizer code in terms of the size of the group of logical operators and the size of the group of stabilizers of the code. Lastly, we provide example of Clifford codes that are not stabilizer codes.
Franz Fuchs
Logical Operations on Invariant Subspaces: A QEC-Inspired View of Structured Quantum Dynamics
Many constrained quantum algorithms are naturally formulated not on the full Hilbert space, but on subspaces selected by algebraic or combinatorial constraints. In this talk, I discuss a quantum-error-correction-inspired perspective on such dynamics, in which feasible and invariant subspaces are regarded as code-like spaces and constraint-preserving evolutions as logical operations acting within them. I focus first on the LX-mixer framework, where stabilizer methods give systematic constructions of subspace-preserving mixers that can be interpreted as logical X-type operations. I then discuss projected Pauli evolutions, including excitation-type operators, as concrete implementations of dynamics restricted to distinguished subspaces. Finally, I consider continuous-time quantum walks on feasible subspaces, where projected Pauli generators, commutation relations, reachability, and the induced feasible-state graph provide a way to analyze how local generators produce nonlocal structure while remaining inside the constrained subspace. The aim is to identify a common mathematical language for constrained quantum optimization and invariant-subspace dynamics using concepts from quantum error correction.
David Jaklitsch
Levin-Wen model and tensor product of Tube algebra representations
The purpose of the talk is to recall the lattice model of Levin-Wen type, relevant in topological quantum computing. Ocneanu's tube algebra plays a central role in this context, where topological excitations are given by irreducible representations. Our recent results explicitly describe the tensor product of tube algebra representations and their braiding. The equivalence between the categories of tube algebra representations and the Drinfeld center category is (by means of this structure) upgraded to a braided monoidal equivalence. This is joint work with Makoto Yamashita.
Marcelo Laca
Nuclearity for Toeplitz C*-algebras of product systems¨
Given a product system of correspondences over a sub-monoid of a group, we show that, under some technical assumptions, the fixed-point subalgebra of the gauge action on the Toeplitz C*-algebra is nuclear if and only if the coefficient algebra is nuclear. When the group is amenable, we conclude that this happens if and only if the Toeplitz algebra itself is nuclear. I will discuss several classes of product systems as applications.
This is joint work with E. G. Katsoulis and C.F. Sehnem.
Magnus Landstad
Coactions of compact groups on Mn
We study coactions of a compact group on a finite-dimensional C*-algebra and show it is associated with a Fell bundle. We also look into when a coaction of a compact group on a matrix algebra is implemented by a unitary operator, and when it is inner. Investigating the existence of effective ergodic coactions on Mn reveals that SO(3) has them, while SU(2) does not. We give explicit examples of the two smallest finite nonabelian groups having effective ergodic coactions on Mn.
Tron Omland
On reduced twisted group C*-algebras corresponding to discrete groups
Over the years, I have collaborated with Erik on several papers concerning twisted group C*-algebras, especially their structural properties and applications. In this talk, I will survey our joint work on reduced twisted group C*-algebras associated with discrete groups, and discuss some open problems and directions for future research.
Eduard Ortega
Protecting quantum information with waves
Quantum computers are extremely sensitive to noise. Tiny perturbations from the environment may destroy the quantum information stored in a physical system, making quantum error correction one of the central challenges in quantum technologies.
In this talk, I will discuss a mathematical framework for continuous-variable quantum error correction inspired by ideas from time–frequency analysis and Gabor theory. The starting point is the Gottesman–Kitaev–Preskill (GKP) code, where quantum information is encoded into wave-like states in phase space and protected against small displacement errors.
I will present recent joint work with Franz Luef in which tools from Gabor analysis, Heisenberg modules, and the Zak transform are used to reinterpret GKP-type codes from a time–frequency perspective. In this framework, lattices in phase space play the role of stabilizers, while Gabor frames provide structured and stable expansions of quantum states. This viewpoint naturally connects error correction with redundancy, localization, and harmonic analysis.
The goal of the talk is to give an accessible overview of how ideas originating in signal analysis and operator algebras can contribute to the mathematical foundations of quantum information and quantum error correction.
John Quigg
Use of monoidal categories to generate representations of product systems over N^k
One approach to identifying the C*-algebra of a product system over N^k is to build a representation of it with the aim of applying the Gauge-Invariant Uniqueness theorem. The main problem is how to build the representation. This is complicated by the commutativity of N^k - so many balanced tensor-product correspondences are isomorphic. I'll show how an abstract categorical result of Fowler-Sims can be used to surmount this obstacle. Joint work with Valentin Deaconu, Menevse Eryuzlu Paulovicks, and S. Kaliszewski.
Alexander Ravnanger
The largest AF-ideal in certain crossed products
Certain regularity properties of C*-algebras have the feature that every C*-algebra admits a largest, possibly trivial, ideal with this property. Examples include approximate finite-dimensionality, nuclearity and postliminarity. In this talk, we present a dynamical description of the largest AF-ideal in a crossed product of a totally disconnected space by a free action of the integers. In the case of the uniform Roe algebra of the integers, this has fascinating connections to topological semigroup theory and coarse geometry.
Hannes Wendt
Quantum harmonic analysis beyond phase space
Quantum harmonic analysis is a framework that applies methods from harmonic analysis to the study of operators. In this talk, I will briefly introduce some basic concepts from the subject and discuss how in a more general setting analogues of operator convolutions arise from trace-preserving actions of locally compact groups on semifinite von Neumann algebras, encompassing both classical convolutions and the orthogonality relations for group representations as special cases.
Makoto Yamashita
Amenable actions of SLn(Qp)
I will report on my joint work in progress with Hannes Wendt. The theory of amenable actions of reductive Lie groups is an interesting framework where the geometry of symmetric spaces meets the theory of random walks. We look at the analogous problem in the p-adic setting, and in particular, for SLn(Qp). This presents an interesting twist due to the “discrete-by-compact-open” decomposition of the relevant spaces, and leads to the Poisson boundary that is bigger than the case of Lie groups.