A review is given on the foundations and applications of non-Hermitian classical and
quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra …

The field of classical stochastic processes forms a major branch of mathematics. Stochastic
processes are, of course, also very well studied in biology, chemistry, ecology, geology …

Tensor-network techniques have recently proven useful in machine learning, both as a tool
for the formulation of new learning algorithms and for enhancing the mathematical …

Quantum network research, is exploring new networking protocols, physics-based hardware
and novel experiments to demonstrate how quantum distribution will work over large …

We present two different methods for modeling non-Markovian quantum light-matter
interactions in waveguide QED systems, using matrix product states (MPSs) and a space …

We introduce a class of quantum non-Markovian processes—dubbed process trees—that
exhibit polynomially decaying temporal correlations and memory distributed across …

The method of choice to study one-dimensional strongly interacting many-body quantum
systems is based on matrix product states and operators. Such a method allows one to …

Effective and efficient forecasting relies on identification of the relevant information
contained in past observations—the predictive features—and isolating it from the rest. When …

In the design of stochastic models, there is a constant trade-off between model complexity
and accuracy. Here we prove that quantum models enable a more favorable trade-off. We …

Isolating past information relevant for future prediction is central to quantitative science.
Quantum models offer a promising approach, enabling statistically faithful modeling while …