The development of quantum computing across several technologies and platforms has
reached the point of having an advantage over classical computers for an artificial problem …

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 Lie-Trotter formula, together with its higher-order generalizations, provides a direct
approach to decomposing the exponential of a sum of operators. Despite significant effort …

How do closed quantum many-body systems driven out of equilibrium eventually achieve
equilibration? And how do these systems thermalize, given that they comprise so many …

We review selected advances in the theoretical understanding of complex quantum many-
body systems with regard to emergent notions of quantum statistical mechanics. We cover …

We review the dynamics after quantum quenches in integrable quantum spin chains. We
give a pedagogical introduction to relaxation in isolated quantum systems, and discuss the …

We review the mathematical speed limits on quantum information processing in many-body
systems. After the proof of the Lieb–Robinson Theorem in 1972, the past two decades have …

One of the most widely known building blocks of modern physics is Heisenberg's
indeterminacy principle. Among the different statements of this fundamental property of the …

The impressive progress in quantum hardware of the last years has raised the interest of the
quantum computing community in harvesting the computational power of such devices …

We consider two related tasks:(a) estimating a parameterisation of a given Gibbs state and
expectation values of Lipschitz observables on this state;(b) learning the expectation values …