Quantum Learning Theory for Bosonic Systems (Winter 2025)

Course Details

This winter school provides a focused introduction to quantum learning theory for bosonic and continuous-variable (CV) systems. Quantum learning theory seeks to understand how efficiently information can be extracted from quantum systems, yet most rigorous guarantees have traditionally been developed in finite-dimensional settings. In contrast, many experimental platforms, particularly those in quantum optics, operate in infinite-dimensional Hilbert spaces where theoretical learning guarantees have remained comparatively underdeveloped.

Recent progress has begun to close this gap by introducing new techniques for learning bosonic states, unitaries, and Hamiltonians under physically realistic constraints. The program will present these developments, explain the conceptual tools that drive them, and highlight emerging open directions at the interface of CV quantum information and quantum learning theory. In addition to bosonic systems, the school will also discuss several related results for fermionic systems.

Prerequisites: Participants are expected to have basic familiarity with quantum information theory and mathematical methods used in theoretical computer science. Knowledge of quantum states, channels, and measurements, as well as introductory concepts from learning theory such as sample complexity and concentration inequalities, will be helpful but not strictly required. Prior exposure to continuous-variable quantum information, including Gaussian states and operations, is advantageous but optional. Motivated students with strong mathematical interest are fully encouraged to participate.

Instructor

Main Organizer: Junseo Lee (Seoul National University, harris.junseo(at)gmail.com)
Invited Lecturers (in alphabetical order):
- Marco Fanizza (Inria, Télécom Paris - LTCI, Institut Polytechnique de Paris)
- Filippo Girardi (Scuola Normale Superiore)
- Vishnu Iyer (University of Texas at Austin)
- Antonio Anna Mele (Freie Universität Berlin)
- Francesco Anna Mele (Scuola Normale Superiore)

Course Policies

TBA.

Announcements

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Lectures

Week	Topic	Lecturer	Readings
1	Course Overview	Junseo Lee	Quantum Learning Theory Zoo
2	Introduction to Quantum Learning Theory and Continuous-Variable Quantum Information	Junseo Lee	Quantum Learning and Complexity Theory (Summer 2025) A survey on the complexity of learning quantum states Quantum information with continuous variables
3	Learning Energy-Constrained States and Bosonic Gaussian States	Francesco Anna Mele	Learning quantum states of continuous-variable systems
4	Trace Distance between Bosonic Gaussian States: Estimation and Applications	TBA.	Optimal estimates of trace distance between bosonic Gaussian states and applications to learning
5	Learning t-Doped Fermionic and Bosonic Gaussian States	Antonio Anna Mele	Efficient Learning of Quantum States Prepared With Few Fermionic Non-Gaussian Gates Learning quantum states of continuous-variable systems
6	Energy-Independent Learning of Bosonic Gaussian States	TBA.	Energy-independent tomography of Gaussian states
7	Gaussianity Testing of Bosonic Quantum States	Filippo Girardi	Is it Gaussian? Testing bosonic quantum states
8	Hamiltonian Learning for Bosonic Gaussian States	Marco Fanizza	Efficient Hamiltonian, structure and trace distance learning of Gaussian states
9	Learning t-Doped Fermionic Unitaries	Vishnu Iyer	Fermion Sampling: A Robust Quantum Computational Advantage Scheme Using Fermionic Linear Optics and Magic Input States Mildly-Interacting Fermionic Unitaries are Efficiently Learnable
10	Learning Bosonic Gaussian Unitaries	Junseo Lee	Efficient learning of bosonic Gaussian unitaries
11	Additional Topics	Junseo Lee	Classical shadow tomography for continuous variables quantum systems Energy, Bosons and Computational Complexity