Quantum stabilizer codes, lattices, and CFTs
Quantum stabilizer codes, lattices, and CFTs
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量子稳定器代码、晶格和 CFT
DOI：
10.1007/jhep03(2021)160
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发表时间：
2021
影响因子：
5.4
通讯作者：
Shapere, Alfred
中科院分区：
文献类型：
--
作者：
Dymarsky, Anatoly;Shapere, Alfred
经典纠错码、欧几里得格和手性共形场理论之间有着丰富的联系。本文证明了稳定型量子纠错码与洛伦兹晶格和非手性cft有关。更具体地说，实自对偶稳定器码可以与偶自对偶洛伦兹格相关联，从而定义Narain cft。我们将得到的理论命名为代码cft，并研究它们的性质。代码CFT的t -对偶变换，在底层代码的层次上，简化为代码等价。利用这种等价，任何稳定器码都可以简化为图码。因此，我们可以用图来表示代码cft。我们研究了中心电荷c= n≤12的码cft，发现了许多有趣的例子。其中有一种非手性e8理论，该理论基于e8的根晶格，将其理解为一个偶自对偶洛伦兹晶格。通过分析所有n≤8个节点的图，我们发现了许多物理上不同的等谱理论对和三元组。我们还构造了许多模不变函数，它们满足CFT配分函数的所有基本性质，但不是任何已知的CFT配分函数。我们考虑了所有码理论的系综平均，计算了相应的配分函数，并讨论了其可能的全息解释。这篇论文以一种独立的方式写成，包括广泛的教学介绍和许多明确的例子。
There is a rich connection between classical error-correcting codes, Euclidean lattices, and chiral conformal field theories. Here we show that quantum error-correcting codes, those of the stabilizer type, are related to Lorentzian lattices and non-chiral CFTs. More specifically, real self-dual stabilizer codes can be associated with even self-dual Lorentzian lattices, and thus define Narain CFTs. We dub the resulting theories code CFTs and study their properties. T-duality transformations of a code CFT, at the level of the underlying code, reduce to code equivalences. By means of such equivalences, any stabilizer code can be reduced to a graph code. We can therefore represent code CFTs by graphs. We study code CFTs with small central charge c= n≤ 12, and find many interesting examples. Among them is a non-chiral E 8 theory, which is based on the root lattice of E 8 understood as an even self-dual Lorentzian lattice. By analyzing all graphs with n≤ 8 nodes we find many pairs and triples of physically distinct isospectral theories. We also construct numerous modular invariant functions satisfying all the basic properties expected of the CFT partition function, yet which are not partition functions of any known CFTs. We consider the ensemble average over all code theories, calculate the corresponding partition function, and discuss its possible holographic interpretation. The paper is written in a self-contained manner, and includes an extensive pedagogical introduction and many explicit examples.
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作者：
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DOI：
--
发表时间：
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期刊：
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