# Strings 2022

Jul 18 – 23, 2022
University of Vienna
Europe/Vienna timezone

## Quantum Complexity as Hydrodynamics

Not scheduled
20m
Audimax (University of Vienna)

### Audimax

#### University of Vienna

Universitätsring 1, 1010 Vienna, Austria

Pablo Basteiro

### Description

As a new step towards defining complexity for quantum field theories, we map Nielsen operator complexity for $SU(N)$ gates to two-dimensional hydrodynamics. We develop a tractable large $N$ limit that leads to regular geometries on the manifold of unitaries as $N$ is taken to infinity. To achieve this, we introduce a basis of non-commutative plane waves for the $\mathfrak{su}(N)$ algebra and define a metric with polynomial penalty factors. Through the Euler-Arnold approach we identify incompressible inviscid hydrodynamics on the two-torus as a novel effective theory of large-qudit operator complexity. For large $N$, our cost function captures two essential properties of holographic complexity measures: ergodicity and conjugate points.

### Presentation materials

There are no materials yet.