We give a pedagogical review of how concepts from quantum information theory build up
the gravitational side of the anti-de Sitter/conformal field theory correspondence. The review …

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 …

We develop a geometric approach to operator growth and Krylov complexity in many-body
quantum systems governed by symmetries. We start by showing a direct link between a …

A bstract We study the operator growth in open quantum systems with dephasing dissipation
terms, extending the Krylov complexity formalism of [1]. Our results are based on the study of …

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 …

A bstract Heisenberg time evolution under a chaotic many-body Hamiltonian H transforms
an initially simple operator into an increasingly complex one, as it spreads over Hilbert …

Krylov complexity, or K-complexity for short, has recently emerged as a new probe of chaos
in quantum systems. It is a measure of operator growth in Krylov space, which conjecturally …