Quantum computational complexity estimates the difficulty of constructing quantum states
from elementary operations, a problem of prime importance for quantum computation …

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” …

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 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 Motivated by recent studies of holographic complexity, we examine the question of
circuit complexity in quantum field theory. We provide a quantum circuit model for the …

In this work, we find that the complexity of quantum many-body states, defined as a spread in
the Krylov basis, may serve as a probe that distinguishes topological phases of matter. We …

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 …

A bstract We evaluate the full time dependence of holographic complexity in various eternal
black hole backgrounds using both the complexity= action (CA) and the complexity= volume …

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 …