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

Abstract The Sachdev–Ye–Kitaev (SYK) model is a strongly coupled, quantum many-body
system that is chaotic, nearly conformally invariant, and exactly solvable. This remarkable …

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 …

We study holographic entanglement entropy in dS/CFT and introduce timelike entanglement
entropy in CFTs. Both of them take complex values in general and are related with each …

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 …

We investigate notions of complexity of states in continuous many-body quantum systems.
We focus on Gaussian states which include ground states of free quantum field theories and …

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 …