Polonez project

Compressed sensing and quantum many-body physics

In both, compressed sensing and quantum many-body physics, a central task is to find and use suitable descriptions of the central degrees of freedom of a signal or system. In fact, also the methods to exploit them are often similar and have lead to breakthrough results in both fields [arXiv:0909.3304, arXiv:0910.1879]. Methods from quantum physics concerning concentration bounds [arXiv:quant-ph/0012127] and tensor network methods and feature strongly in compressed sensing and, also the other way around, compressed sensing methods are crucial in the reduction of the measurement effort in tomographic tasks in quantum physics. Also convex optimization methods are important (proof) tools in both fields. The underlying idea of this project is to used synergy effects when working in both fields simultaneously.

Topics of the Polonez project

• Compressed sensing

• Quantum tomography

• Simulation of open quantum systems

• Quantum thermodynamics

Publications

• Properties of thermal quantum states: locality of temperature, decay of correlations, and more

• Recovering quantum gates from few average gate fidelities

• On products of Gaussian random variables

• Fidelity witnesses for fermionic quantum simulations

• Guaranteed recovery of quantum processes from few measurements

• Note on the saturation of the norm inequalities between diamond and nuclear norm

• Reliable recovery of hierarchically sparse signals and application in machine-type communications

Host

I am grateful to my host institution:

University of Gdańsk / Institute of Theoretical Physics and Astrophysics / Quantum Information Center in Gdańsk (KCIK)

Acknowledgment

This Polonez project is financed by the National Science Centre Poland (Polonez 2015/19/P/ST2/03001) within the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 665778.