Recent years have witnessed an explosion of interest in quantum devices for the production,
storage, and transfer of energy. This Colloquium concentrates on the field of quantum …

We propose a measure of quantum state complexity defined by minimizing the spread of the
wave function over all choices of basis. Our measure is controlled by the “survival amplitude” …

A bstract We apply a notion of quantum complexity, called “Krylov complexity”, to study the
evolution of systems from integrability to chaos. For this purpose we investigate the …

A bstract Krylov complexity measures the spread of the wavefunction in the Krylov basis,
which is constructed using the Hamiltonian and an initial state. We investigate the evolution …

A bstract Inspired by the universal operator growth hypothesis, we extend the formalism of
Krylov construction in dissipative open quantum systems connected to a Markovian bath …

A bstract In semi-classical systems, the exponential growth of the out-of-time-order correlator
(OTOC) is believed to be the hallmark of quantum chaos. However, on several occasions, it …

Krylov complexity is a measure of operator complexity that exhibits universal behavior and
bounds a large class of other measures. In this paper, we generalize Krylov complexity from …

A bstract Quantum complexity, suitably defined, has been suggested as an important probe
of late-time dynamics of black holes, particularly in the context of AdS/CFT. A notion of …

We show that out-of-time-order correlators (OTOCs) constitute a probe for local-operator
entanglement (LOE). There is strong evidence that a volumetric growth of LOE is a faithful …

In an isolated system, the time evolution of a given observable in the Heisenberg picture can
be efficiently represented in Krylov space. In this representation, an initial operator becomes …