• Open Access

Quantum complexity as hydrodynamics

Pablo Basteiro, Johanna Erdmenger, Pascal Fries, Florian Goth, Ioannis Matthaiakakis, and René Meyer
Phys. Rev. D 106, 065016 – Published 14 September 2022
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Abstract

As a new step toward 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 noncommutative plane waves for the 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.

  • Figure
  • 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

Physics Subject Headings (PhySH)

Particles & Fields

Authors & Affiliations

Pablo Basteiro1, Johanna Erdmenger1, Pascal Fries1, Florian Goth1, Ioannis Matthaiakakis1,2, and René Meyer1,*

  • 1Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Julius-Maximilians-Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
  • 2Dipartimento di Fisica, Università di Genova and I.N.F.N.—Sezione di Genova, via Dodecaneso 33, I-16146 Genova, Italy

  • *Corresponding author. rene.meyer@physik.uni-wuerzburg.de

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Issue

Vol. 106, Iss. 6 — 15 September 2022

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