Andreas Bluhm

Thanks to Eric Evert, Igor Klep, Victor Magron and Ion Nechita for the interesting collaboration. I certainly learned a lot!

For this, we need to study different types of extreme points for matrix convex sets and uncover a surprising difference between real and complex matrix convex sets.

Inclusion constants for free spectrahedra with applications to quantum incompatibility Building on the matrix cube problem, inclusions of free spectrahedra have been used successfully to obtain relaxations of hard spectrahedral inclusion problems. The quality of such a relaxation is qua...

Just in time for the holidays: We have a new paper out about how to use techniques from non-commutative polynomial optimization for measurement incompatibility: scirate.com/arxiv/2512.1...

Learning Coulomb Potentials and Beyond with Fermions in Continuous Space We present a modular algorithm for learning external potentials in continuous-space free-fermion models including Coulomb potentials in any dimension. Compared to the lattice-based approaches, the con...

New preprint on Hamiltonian Learning of Coulomb potentials and smooth potentials in continuous space

arxiv.org/abs/2510.08471

Thanks to my collaborators, @hippoquantus.bsky.social , Tim Möbus, and Oliver Siebert!

A big thanks to my coauthors for the great collaboration! Hopefully you enjoy reading the paper as much as we did writing it, despite the approaching QIP deadline :)

Again, this result generalizes to k-local Hamiltonians for k>2. While the algorithm is sample- and time-efficient, we don't know if it is optimal, because we lack matching lower bounds so far. So we ask: What is the optimal sample-complexity of
certifying Ising Gibbs states?

Some Recent Progress in Learning Theory: The Quantum Side

In our final result, we give an algorithm for certifying Ising Gibbs
states in trace norm that is both sample and time-efficient, thereby solving a question posed by Anshu hdsr.mitpress.mit.edu/pub/3x2sd8nq...

This one actually generalizes to k-local and does not need any additional assumptions (e.g. on the degree of the interaction graph). Whether one can find a better algorithm that is also time efficient is an interesting open problem.

Secondly, we design an algorithm for learning Ising Gibbs states in trace norm that is sample-efficient in all parameters. Previous approaches learned the underlying Hamiltonian (which implies learning the Gibbs state) but suffered from exponential sample complexity in the inverse temperature.

To our knowledge, this is the first nearly-optimal algorithm for testing a Hamiltonian property. A key ingredient in our analysis is the Bonami Lemma from Fourier analysis. Curiously, this Lemma is the reason that our results do not seem to easily generalize to k-local Hamiltonians for k>2.

First, we show that certifying an Ising Hamiltonian (checking whether it is identical to some H_0 or far from it) in
normalized Frobenius norm via access to its time-evolution operator requires only O(1/ε) evolution time. This matches the known lower bounds up to a logarithmic factor.

Certifying and learning quantum Ising Hamiltonians In this work, we study the problems of certifying and learning quantum Ising Hamiltonians. Our main contributions are as follows: Certification of Ising Hamiltonians. We show that certifying an Ising ...

Happy to announce our new paper "Certifying and learning quantum Ising Hamiltonians" scirate.com/arxiv/2509.1..., together with Matthias C. Caro, Francisco Escudero Gutiérrez, Aadil Oufkir, and Cambyse Rouzé. We are focusing in this paper on 2-local Hamiltonians (so a bit more general than Ising).

The QIP 2026 call for papers is out! QIP 2026 will be held in Riga, Latvia from January 24–30, 2026. See you there!
qip2026.lu.lv

I am currently looking for a PhD student who would like to work on position-based cryptography. Details can be found here: andreasbluhm.eu/wp-content/u...

Please spread the word!

Thanks to Tim Möbus, Tuvia Gefen, Yu Tong, Albert H. Werner and Cambyse Rouzé for the great collaboration!

Our main technical tool is a new adiabatic approximation for general Lindbladian evolutions with unbounded generators which should also be helpful elsewhere. For example, we can quantify with it how photon-driven dissipation leads to an effective evolution on the code space for bosonic cat codes.

Heisenberg-limited Hamiltonian learning for interacting bosons We develop a protocol for learning a class of interacting bosonic Hamiltonians from dynamics with Heisenberg-limited scaling. For Hamiltonians with an underlying bounded-degree graph structure, we can...

Before, we could either do Heisenberg-limited learning for Bose-Hubbard type models scirate.com/arxiv/2307.0..., or learn arbitrary Hamiltonians with engineered dissipation, but not with Heisenberg scaling scirate.com/arxiv/2307.1.... Our new paper shows that you can have the best of both worlds.

Heisenberg-limited Hamiltonian learning continuous variable systems via engineered dissipation Discrete and continuous variables oftentimes require different treatments in many learning tasks. Identifying the Hamiltonian governing the evolution of a quantum system is a fundamental task in quant...

New day, new paper, this time on Heisenberg-limited Hamiltonian learning for continuous variable systems with engineered dissipation: scirate.com/arxiv/2506.0.... The idea is to use strong dissipation to restrict the Hamiltonian evolution onto a convenient subspace where we can learn it.

Thanks to my PhD student Simon Höfer, Alex May, Mikka Stasiuk, Philip Verduyn Lunel and @henryyuen.bsky.social for the great collaboration! And congratulations to Simon for his first paper.

In the longer term, our aim is to be able to put NLQC tasks into classes of equally hard problems, like complexity classes. This would allow us to identify the hard NLQC problems that we would like to use for quantum position verification, because they are hard for attackers to solve.

In particular, we have shown that two protocols for quantum position verification, the f-route and the f-measure protocol, are equally secure, i.e., if you can attack one, you can attack the other. This gives the first subexponential upper bound on the entanglement needed to attack f-measure.

A complexity theory for non-local quantum computation Non-local quantum computation (NLQC) replaces a local interaction between two systems with a single round of communication and shared entanglement. Despite many partial results, it is known that a cha...

We have a new preprint out on the topic of quantum position verification and non-local quantum computation (NLQC): scirate.com/arxiv/2505.2.... We are comparing different NLQC tasks and find reductions between them (in the sense of if I can do task 1, then I can do task 2 with an extra EPR pair).

Liste des postes de chaires de professeur junior de CNRS Sciences informatiques 2025 Le CNRS recrute des chercheurs et chercheuses sur des Chaires de professeur junior (CPJ) dans plusieurs domaines relatifs aux sciences informatiques.

CNRS is opening a call for CPJ (chair de professeur junior), a kind of tenure track with very good conditions. One position is open for quantum computing, and one of the hosting labs is LIG in beautiful Grenoble! The application deadline is July 14th.

www.ins2i.cnrs.fr/fr/cnrsinfo/...

Thanks to my coauthors for the great collaboration!

To unite these different phenomena, we consider multimeters, i.e., collections of measurements. Many of them, e.g., compatible measurements, classical simulations of measurements, or the compression of measurements can be viewed as factorizations of these multimeters through different state spaces.

Factorization of multimeters: a unified view on nonclassical quantum phenomena Quantum theory exhibits various nonclassical features, such as measurement incompatibility, contextuality, steering, and Bell nonlocality, which distinguish it from classical physics. These phenomena ...

If you are interested in quantum non-classicality, you might enjoy our new preprint: scirate.com/arxiv/2504.1.... In it, we use the framework of general probabilistic theories to connect different forms of non-classicality, in particular measurement incompatibility, steering, and Bell non-locality.

FZ Jülich is hiring a PhD candidate which will be co-supervised by myself at U Cologne. Interested in benchmarking/characterisation, in working in a highly collaborative environment, and want to see your work being used in experiments? Consider applying!
www.fz-juelich.de/en/careers/j...

Master in Mathematical Physics

If you're an undergraduate student interested in the mathematics of quantum physics and general relativity, consider the

Tübingen International M.Sc. Program in #MathematicalPhysics

www.math.uni-tuebingen.de/en/mmp

Opens for applications today

Summer school Mathematics and Physics of Quantum Computing and Quantum Learning, on the island of Porquerolles, France

www.quantiki.org/conference/m...

PhD Opportunities – Quantum Algorithms for Quantum Chemistry. Join the Quantum for Life Center at the University of Copenhagen as PhD student! Work on quantum algorithms for chemistry with Prof. Matthias Christandl & co-supervision by Prof. Markus Reiher (ETH Zurich). 1/n