%0 Journal Article %1 PhysRevD.106.065016 %A Basteiro, Pablo %A Erdmenger, Johanna %A Fries, Pascal %A Goth, Florian %A Matthaiakakis, Ioannis %A Meyer, René %D 2022 %I American Physical Society %J Phys. Rev. D %K a %N 6 %P 065016 %R 10.1103/PhysRevD.106.065016 %T Quantum complexity as hydrodynamics %U https://link.aps.org/doi/10.1103/PhysRevD.106.065016 %V 106 %X 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.

@article{PhysRevD.106.065016, 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.}, added-at = {2022-09-26T12:12:25.000+0200}, author = {Basteiro, Pablo and Erdmenger, Johanna and Fries, Pascal and Goth, Florian and Matthaiakakis, Ioannis and Meyer, Ren\'e}, biburl = {https://www.bibsonomy.org/bibtex/22aa46958cf57e5081c91cd636eabed57/ctqmat}, day = 14, description = {Phys. Rev. D 106, 065016 (2022) - Quantum complexity as hydrodynamics}, doi = {10.1103/PhysRevD.106.065016}, interhash = {b01cce837c01c1e92a9fa4846e3060a0}, intrahash = {2aa46958cf57e5081c91cd636eabed57}, journal = {Phys. Rev. D}, keywords = {a}, month = sep, number = 6, numpages = {7}, pages = 065016, publisher = {American Physical Society}, timestamp = {2023-01-16T14:49:29.000+0100}, title = {Quantum complexity as hydrodynamics}, url = {https://link.aps.org/doi/10.1103/PhysRevD.106.065016}, volume = 106, year = 2022 }