EF1 – Extracting Dynamical Laws from Complex Data



Quantum machine learning

Project Heads

Jens Eisert, Klaus-Robert Müller

Project Members

Frederik Wilde (FU) 

Project Duration

01.01.2019 – 31.12.2021

Located at

FU Berlin


One of the core tools used and developed in MATH+ is that of machine learning. This project suggests a concerted research program in a highly promising and novel kind of machine learning, that of quantum machine learning, in several flavors. Emphasis is on mathematical and conceptual method development, coordinated and in collaboration with other machine learning efforts in MATH+, taking a rigorous perspective. Results along these line of thought are improved quantum stochastic gradient methods with full recovery guarantees. However, a range of applications, ranging from communication technology to condensed-matter physics, will be explored as well.

Project Webpages

Selected Publications

  • Stochastic gradient descent for hybrid quantum-classical optimization, R. Sweke, F. Wilde, J. Meyer, M. Schuld, P. K. Fährmann, B. Meynard-Piganeau, J. Eisert, arXiv:1910.01155 (2019).
  • Expressive power of tensor-network factorizations for probabilistic modeling, with applications from hidden Markov models to quantum machine learning, I. Glasser, R. Sweke, N. Pancotti, J. Eisert, J. I. Cirac, Advances in Neural Information Processing Systems 32, Proceedings of the NeurIPS 2019 Conference (2019).
  • Tensor network approaches for learning non-linear dynamical laws, A. Goeßmann, M. Götte, I. Roth, R. Sweke, G. Kutyniok, J. Eisert, arXiv:2002.12388 (2020).
  • Quantum certification and benchmarking, J. Eisert, D. Hangleiter, N. Walk, I. Roth, D. Markham, R. Parekh, U. Chabaud, E. Kashefi, arXiv:1910.06343, Nature Reviews Phys. (2020).
  • A variational toolbox for quantum multi-parameter estimation, J. Jakob Meyer, J. Borregaard, J. Eisert, in preparation (2020).
  • On the quantum learnability of discrete distributions, R. Sweke, J.-P. Seifert, D. Hangleiter, J. Eisert, in preparation (2020).
  • Unifying machine learning and quantum chemistry – a deep neural network for molecular wavefunctions, K. T. Schütt, M. Gastegger, A. Tkatchenko, K. -R. Müller, R. J. Maurer, arXiv:1906.10033.

Selected Pictures

Quantum stochastic gradients
This work shows how stochastic gradients based on single-shot measurements can be transferred to the quantum regime to improve variational quantum algorithms and notions of quantum-enhanced machine learning, equipped with fully rigorous recovery guarantees.

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