Abstract
As a new step toward defining complexity for quantum field theories, we map Nielsen operator complexity for gates to two-dimensional hydrodynamics. We develop a tractable large limit that leads to regular geometries on the manifold of unitaries as is taken to infinity. To achieve this, we introduce a basis of noncommutative plane waves for the 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 , our cost function captures two essential properties of holographic complexity measures: ergodicity and conjugate points.
- Received 10 March 2022
- Accepted 7 August 2022
DOI:https://doi.org/10.1103/PhysRevD.106.065016
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
Published by the American Physical Society