My general research interest is developing new techniques in (quantum) algorithms and the mathematical analysis of their properties. I am particularly interested in understanding how quantum algorithms behave on typical instances. Below, I introduce the topics I think about most right now.
Smoothed Complexity for Quantum Algorithms
In practice, problem instances are often determined by some measurement process, which is naturally subject to noise. Formalizing this insight, smoothed analysis studies the change in complexity when adversarial worst-case inputs are subject to small random perturbations. Instead of choosing a distribution from which typical instances are sampled, one merely has to pick an appropriate noise model for the problem instances. This makes for much more realistic assumptions! Picking a suitable noise model for some measurement process determining your problem instances is much easier than magically inferring from what distribution your instances are sampled. Smoothed complexity is especially successful in explaining the practical behavior when the worst-case complexity is driven by pathological and unstable spectral or geometric features. This perspective has had major impact in classical algorithms, but its systematic use in quantum information remains limited.
Sublinear-Time Compressed Sensing in Quantum Information
In signal processing, a natural way to parametrize the complexity of signals is via their compressibility, with typical signals in application often having some compressible structure. Standard compressed sensing algorithms, while requiring only a sublinear number of measurements, still demand computational time that is at least linear in the ambient dimension d. There is a powerful but less explored class of algorithms that achieves both sublinear measurement count and sublinear computational runtime, scaling as \mathrm{poly}(s, \log d) for s-sparse signals. In the recent years, there have been huge advances in this area, culminating in this result from Fischer and Nakos. The interplay between these techniques and quantum information theory is essentially unexplored.
My related research:
Franz J. Schreiber, Jens Eisert, Johannes Jakob Meyer, Tomography of Parametrized Quantum States, PRX Quantum 6, 020346 (2025)
–> We show how to lift a broad class of tomographic procedures (full tomography, shadow tomography etc.) to perform tomography of parametrized states (and channels). Uses standard compressed sensing, making this work with sub-linear time algorithms would be very nice. This would allow for exponentially large ansätze for the parametrization. Right now, we circumvent the need for this with (in my opinion reasonable) assumptions on the model problems we consider.
Super-quadratic Quantum Speedups for Combinatorial Optimization
Most combinatorial optimization tasks of interest are NP-complete, which makes super-polynomial quantum advantages highly unlikely. However, a sufficiently large polynomial speedup on the right problem would be of pronounced economic relevance. What constitutes “sufficiently large” in this context? This depends on the concrete clock times for applying gates, readout etc. of future quantum devices. Estimates suggest that a quartic speedup might be enough to translate into a real world advantage. Notably, not many such speedups are known, most are only quadratic. For NP-hard problems, there are no super-quadratic speedups known today.
As a first step, I would be happy with a super-quadratic speedup on any (natural) NP-hard problem, which would already constitute a breakthrough. Going beyond quadratic is a natural barrier here, as quadratic speedups can be achieved for many problems using Grovers algorithm. Not all NP-hard problems are suitable candidates for this program. The quadratic advantage from Grovers algorithm is known to be optimal in the black-box setting. Under the widely believed strong exponential time hypothesis (SETH), the satisfiability problem (SAT) cannot be solved faster than with brute-force search. In other words, SAT is believed to contain no additional structure that can be algorithmically exploited compared to the black-box search setting, such that the quadratic speedup obtained with Grovers algorithm is likely optimal here. Using reductions to SETH, conditional lower bounds of the same type have been established for a number of other problems.
For many other NP-hard problems, however, there is additional structure compared to the black-box setting. A prime example is 3-SAT, both in terms of theoretical and practical interest. 3-SAT, while being NP-hard, clearly admits additional structure, as evidenced by e.g. Schoenings algorithm which runs significantly faster than brute-force search. Can this additional structure be used to obtain more than a quadratic speedup on such problems? To date, there are no complexity theoretic obstruction to this, which calls for either better algorithms or new hardness conjectures.
My related research:
Franz J. Schreiber, Maximilian J. Kramer, Alexander Nietner, Jens Eisert, A measurement-driven quantum algorithm for SAT: Performance guarantees via spectral gaps and measurement parallelization, arXiv:2511.09647 (2025)
–> We investigate a numerically promising quantum 3-SAT solver that seems to have an “inherently quantum” mechanism, as opposed to amplitude-amplification on top of a classical solver. Determining the exact worst-case runtime of the solver proves to difficult, but we manage to reduce the problem to determining the spectral gap of special family of Hamiltonians. We also give some technical improvements of the algorithms, most interestingly a perfect hash family-based parallelization scheme.
Other works
I have also done research on other topics, in particular quantum machine learning.
Pablo Rodriguez-Grasa, Matthias C. Caro, Jens Eisert, Elies Gil-Fuster, Franz J. Schreiber, Carlos Bravo-Prieto, A PAC-Bayesian approach to generalization for quantum models, arXiv:2603.22964 (2026)
Erik Recio-Armengol, Franz J. Schreiber, Jens Eisert, Carlos Bravo-Prieto, Learning complexity gradually in quantum machine learning models, arXiv:2411.11954 (2024)
Franz J. Schreiber, Jens Eisert, Johannes Jakob Meyer, Classical Surrogates for Quantum Learning Models, Phys. Rev. Lett. 131, 100803 (2023)
–> My first ever paper! We define the notion of a “classical surrogate” for quantum learning models. That is, we observe that after training (so for fixed weights), for some quantum models, there is an efficient process to construct a classical representation of the model, a so-called classical surrogate. There has been lots of follow up and related work, see for example Jerbi et al. which I quite liked.