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arXiv 2109.01152hep-th
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流体力学的量子复杂性

Quantum Complexity as Hydrodynamics

Pablo Basteiro, Johanna Erdmenger, Pascal Fries, Florian Goth, Ioannis Matthaiakakis, René Meyer

备注：
17 pages, 4 figures, v2 corrected results on sectional curvatures, further details about large N decoupling limit added
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摘要：

作为一个新的一步，定义量子场论的复杂性，我们映射到二维流体力学的$SU(N)$门的尼尔森算子复杂性。我们开发了一个易于处理的大$N$限制，导致经常几何上的酉流形作为$N$被带到无穷大。为了实现这一点，我们引入了一个基础的非交换平面波的$\mathfrak{su}(N)$代数，并定义了一个度量与多项式罚因子。通过Euler-Arnold方法，我们确定了不可压缩的无粘流体动力学的两个环面作为一种新的有效的理论的大qudit运营商的复杂性。对于大的$N$，我们的成本函数捕获全息复杂性措施的两个基本属性：遍历性和共栖点。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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