Here I collect lecture notes, recordings, and other materials from courses and invited lectures I have taught.
Quantum Learning Theory for Bosonic and Fermionic Systems
EPFL Bernoulli Center · May 2026 · Invited tutorial
Invited tutorial at the program Intersection of Quantum Learning Theory, Quantum Sensing, and Quantum Verification, covering recent approaches to learning structured bosonic and fermionic quantum systems.
Lecture notes — Quantum Learning Theory for Bosonic and Fermionic Systems (PDF)
Also: Video · Program
Learning $t$-doped Fermionic and Bosonic Gaussian States
QISCA Winter School · January 2026 · Invited lecture
Invited lecture for the Quantum Learning Theory for Bosonic and Fermionic Systems winter school, on learning Gaussian quantum systems perturbed by a small amount of non-Gaussianity.
Materials: Lecture notes · Video · Course
Related work: Fermionic systems · Bosonic systems
Haar Integration Tools in Quantum Information
AIMS · Cape Town · October 2025 · Invited lecturer (4 hours)
Tutorial at the 1st AIMS Workshop and School on The Theory of Quantum Learning Algorithms, introducing Haar integration, moment operators, and their applications throughout quantum information and quantum learning.
Materials: Program · Tutorial article
Representation Theory for Quantum Information Science
QMATH · University of Copenhagen · August 2025 · Invited lecturer (12 hours)
I gave six blackboard lectures across the QMATH Tutorial and Masterclass on Representation Theory in Quantum Information Science, beginning with a self-contained introduction to representation theory and then developing applications to Haar integration and the Clifford group.
I. Representation theory
For the introductory part, I prepared a self-contained set of lecture notes developing the representation-theoretic tools most useful in quantum information. The notes are intended to be accessible without prior background in representation theory.
📘 Lecture notes
Representation Theory for Quantum Information Science — Download PDF
The notes cover:
- Groups, cosets, and group actions
- Representations of finite groups and Maschke’s theorem
- Schur’s lemma and commutants
- Character theory and orthogonality relations
- Fourier analysis on finite groups
- Schur–Weyl duality and applications to quantum information
- Compact groups and tensor-product representations
II. Haar integration
The second part focused on Haar integration, moment operators, and techniques for computing averages over random quantum states and unitaries, following my tutorial article:
Introduction to Haar Measure Tools in Quantum Information: A Beginner’s Tutorial
III. The Clifford commutant
The final part developed representation-theoretic methods for understanding the Clifford group and its commutant, drawing on our work:
A complete theory of the Clifford commutant · Slides
Course archive
Quantum Information — Freie Universität Berlin
2022–23 · Tutorials
I taught tutorials for the Quantum Information Theory course at Freie Universität Berlin. Below are the problem sheets, my solutions, and additional notes prepared for the tutorials.
Exercises and solutions
- Problem Sheet 0 — Warm-up: Sheet · Solutions
- Problem Sheet 1 — Density matrices and Bell experiments: Sheet · Solutions
- Problem Sheet 2 — POVMs and encoding classical information: Sheet · Solutions
- Problem Sheet 3 — Quantum teleportation and $p$-norms: Sheet · Solutions
- Problem Sheet 4 — Graphical calculus and quantum channels: Sheet · Solutions
- Problem Sheet 5 — Quantum channels and entropy: Sheet · Solutions
- Problem Sheet 6 — Operator properties and LOCC: Sheet · Solutions
- Problem Sheet 7 — Capacities and majorization: Sheet · Solutions
- Problem Sheet 8 — Entanglement witnesses and cryptography: Sheet · Solutions
- Problem Sheet 9 — Quantum Fourier transform and stabilizers: Sheet · Solutions
- Problem Sheet 10 — Stabilizers and quantum gates: Sheet · Solutions
- Problem Sheet 11 — Measurement-based quantum computing: Sheet · Solutions
Additional tutorial notes
- PVMs, POVMs, and Naimark’s dilation theorem
- Quantum channel theorems
- Simple proofs of the Schmidt and Kraus decompositions
- Classical entropies
- Quantum entropies
- Basics of quantum computing
- Stabilizer formalism
Recommended references
The main course page contains the lecture notes for the course by Jens Eisert.
For complementary treatments, I recommend the following references.
- Michael M. Wolf — Quantum Channels & Operations: A Guided Tour
- John Preskill — Quantum Computation lecture notes
- Joseph M. Renes — Quantum Information Theory lecture notes
- Ronald de Wolf — Quantum Computing: Lecture Notes
- Andrew M. Childs — Lecture Notes on Quantum Algorithms
- Philippe Faist — Quantum Error Correction lecture notes
- Daniel Gottesman — Surviving as a Quantum Computer in a Classical World
- Michael A. Nielsen and Isaac L. Chuang — Quantum Computation and Quantum Information
- Mark M. Wilde — From Classical to Quantum Shannon Theory
- Thomas M. Cover and Joy A. Thomas — Elements of Information Theory
Questions about the material are always welcome — get in touch.