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

Quantum Complexity as Hydrodynamics

Not scheduled
4m
Audimax (University of Vienna)

Audimax

University of Vienna

Universitätsring 1, 1010 Vienna, Austria
Gong Show Talk Gong Show

Speaker

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.

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